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T
PARADISE OF CHILDHOOD
A MANUAL FOR SELF-INSTRUCTION IN FRIEDRICH FROEBEL'S
EDUCATIONAL PRINCU'LES,
AXD A ntACTICAL
Glide to Kinder-Gartners.
EDWARD WIEBE.
WITH SEVENTY- FOUR PLATES OF ILLUSTRATIONS.
c/
MILTON BRADLEY & COMPANY,
SPRINGFIKLD, MASS.
Lbins
Entered according to Act of Congress, in the year 1869, by
MILTON BRADLEY & COMPANY,
the Clerk's Office of the District Court of the District of Massachusetts.
SAMUEL BOWLES AND COMPANY,
PRINTERS, ELECTKOTYPERS, AND BINDERS,
SPRINGFIELD, MASS.
ERRATA.
PI,ATE XI. Fir.. i6. — Upper row to consist of four whole cubes.
Fig 19. — In the second row the 2nd and 4th square, on either side should be open, so as to repre-
sent windows.
Fig. 21.— The remaining whole cube is to be placed upon the center in the first row.
PLATE XIII, Fig. 30. — Eight quarter blocks should be connected here with the four outermost whole blocks as
in figures 28 and 29.
PLATE XIV, Fig 51. — Six quarter cubes form star in center as in figure 52.
PLATE XVII, Fig. 3. — The blocks forming back wall should stand on those forming foundation.
PLATE XIX, Fig. 3. — The four corner pieces are to be like those in figure 2
PLATE XX, Fig. 21 in the perspective should extend in front over six squares only.
Fig. 23. — There should be an open space in the center of two squares, one above the other.
PLATE XXII, Fig. 117. — Left upper part should be shaded like the right lower one.
PLATE XLVI, Fig. 5. — The two halves of the figure ought to connect as in figure 4.
INTRODUCTION.
Until a recent period, but little interest has been
felt by people in this country, with regard to the
Kinder-Garten method of instruction, for the simple
reason that a correct knowledge of the system has
never been fully promulgated here. However the lec-
tures of Miss E. P. Peabody of Cambridge, Mass.,
have awakened some degree of enthusiasm upon the
subject in different localities, and the establishment
of a few Kinder-Garten schools has served to call forth
a more general inquiry concerning its merits.
We claim that every one who believes in rational
education, will become deeply interested in the pecu-
liar features of the work, after having become ac-
quainted with Froebel's principles and plan ; and
that all that is needed to enlist the popular sentiment
in its favor is the establishment of institutions of this
kind, in this country, upon the right basis.
With such an object in view, we propose to present
an outline of the Kinder-Garten plan as developed by
its originator in Germany, and to a considerable ex-
tent by his followers in France and England.
But as Froebel's is a system which must be carried
out faithfully in all its important features, to insure
success, we must adopt his plan as a whole and carry
it out with such modifications of secondary minutia;
only, as the individual case may acquire without vio-
lating its fundamental principles. If this cmnot be
accomplished, it were better not to attempt the task
at all.
The present work is entitled a Manual for Self-
Instruction and a Practical Guide for Kinder-Gartners.
Those who design to use it for either of these pur-
poses, must not expect to find in it all that they ought to
know in order to instruct the young successfully ac-
cording to Froebel's principles. No book can ever
be written which is able to make a perfect Kinder-
Gartner ; this requires the training of an able teacher
actively engaged in the work at the moment
" Kinder-Garten Culture," says Miss Peabody, in the
preface to her "Moral Culture of Infancy," "is the
adult mind entering into the child's world and ap-
preciating nature's intention as displayed in every
impulse of spontaneous life, so directing it that the
joy of success may be ensured at every step, and
artistic things be actually produced, which gives the
selfreliance and conscious intelligence that ought to
discriminate human power from blind force."
With this thought constantly present in his mind,
the reader will find, in this book, all that is indispens-
ably necessary for him to know, from the first estab-
lishment of the Kinder-Garten through all its various
degrees of development, including the use of the mate-
rials and the engagement in such occupations as are
peculiar to the system. There is much more, how-
ever, that can be learned only by individual obser-
vation. The fact, that here and there, persons, pre-
suming upon the slight knowledge which they may
have gained of Froebel and his educational principles,
from books, have established schools called Kinder-
Gartens, which in reality had nothing in common with
the legitimate Kinder-Garten but the name, has caused
distrust and even opposition, in many minds towards
everything that pertains to this method of instruc-
tion. In discriminating between the spurious and the
real, as is the design of this work, the author would
mention with special commendation, the Educational
IV
INTRODUCTION.
Institute conducted by Mrs. and Miss Kriege in
Boston. It connects with the Kinder-Garten proper,
a Training School for ladies, and any one who wishes
to be instructed in the correct method, will there be
able to acquire the desired knowledge.
Besides the Institute just mentioned, there is one
in Springfield, Mass., under the supervision of the
writer, designed not only for the instruction of classes
of children in accordance with these principles, but
also for imparting information to those who are de-
sirous to become Kinder-Gartners. From this source,
the method has already been acquired in several in-
stances, and as one result, it has been introduced into
two of the schools connected with the State Institu-
tion at Monson, Mass.
The writer was in early life acquainted with Froebel ;
and his subsequent experience as a teacher has only
served to confirm the favorable opinion of the system,
which he then derived from a personal knowledge of
its inventor. A desire to promote the interests of true
education, has led him to undertake this work of inter-
pretation and explanation.
Withput claiming for it perfection, he believes that,
as a guide, it will stand favorably in comparison with
any publication upon the subject in the English or the
French language.
The German of Marenholtz, Goldammer, Morgen-
stern and Froebel have been made use of in its prep-
aration, and though new features have, in rare cases
only, been added to the original plan, several changes
have been made in minor details, so as to adapt this
mode of instruction more readily to the American
mind. This has been done, however, without omit-
ting aught of that German thoroughness, which char-
acterizes so strongly every feature of Froebel's system.
The plates accompanying this work are reprints
from " Goldammer's Kinder-Garten," a book recently
published in Germany.
The Paradise of Childhood :
A GUIDE TO KINDER-GARTNERS.
ESTABLISHMENT OF A KINDER-GARTEN.
The requisites for the establishment of a
" Kinder-Garten " are the following :
1. A house, containing at least one large
room, spacious enough to allow the children,
not only to engage in all their occupations,
both sitting and standing, but also to practice
their movement plays, which, during inclem-
ent seasons, must be done in-dcors.
2. Adjoining the large room, one or two-
smaller rooms for sundry purposes.
3. A number of tables, according to the
size of the school, each table affording a
smooth surface ten feet long and four feet
wide, resting on movable frames from eighteen
to twenty-four inches high. The table should
be divided into ten equal squares, to accom-
modate as many pupils ; and each square
subdivided into smaller squares of one inch,
to guide the children in many of their occu-
pations. On either side of the tables should
be settees with folding seats, or small chairs
ten to fifteen inches high. The tables and
settees should not be fastened to the floor, as
they will need to be removed at times to
make room for occupations in which they are
not used.
4. A piano-forte for gjmnastic and musical
exercises — the latter being an important feat-
ure of the plan, since all the occupations are
interspersed with, and many of them accom-
panied by, singing.
5. Various closets for keeping the apparatus
and work of the children — a wardrobe, wash-
stand, chairs, teacher's table, &c.
The house should be pleasantly located,
removed from the bustle of a thoroughfare,
and its rooms arranged with strict regard to
hygienic principles. A garden should sur-
round or, at least, adjoin the building, for
frequent out door exercises, and for gardening
purposes. A .=niall plot is assigned to each
child, in which he sows the seeds and culti-
vates the plants, receiving, in due time, the
flowers or fruits, as the result of his industry
and care.
When a Training School is connected with
the'Kinder-Garten, the children of the "Gar-^
ten " are divided into groups of five or ten —
each group being assisted in its occupations
by one of the lady pupils attending the Train-
ing School.
Should there be a greater number of such
assistants than can be conveniently occupied
in the Kinder Garten, they may take turns
with each other. In a Training School of
this kind, under the charge of a competent
director, ladies are enabled to acquire a thor-
ough and practical knowledge of the system.
They should bind themselves, however, to
remain connected with the institution a speci-
fied time, and to follow out the details of the
method patiently, if they aim to fit themselves
to conduct a Kinder-Garten with success.
In any establishment of more than twenty
children, a nurse should be in constant at-
tendance. It should be her duty also to
preserve order and cleanliness in the rooms,
and to act as janitrix to the institution.
MEANS AND WAYS OF OCCUPATION
IN THE KINDER-GARTEN.
Before entering into a description of the
various means of occupation in tlie Kinder-
Garten, it will be proper to state that Fried-
rich Froebel, the inventor of this system of
education, calls all ocaipations in the Kinder-
Garten '■^ plays" and the materials for occupa-
tion '■^ gifts." In these systematically-arranged
plays, Froebel starts from the fundamental
idea that all education should begin with a
development of the desire for activity innate
in the child; and he has been, as is universally
acknowledged, eminently successful in this
part of his important work. Each step in
the course of training is a logical sequence
of the preceding one ; and the various means
of occupation are developed, one from another,
in a perfectly natural order, beginning with the
simplest and concluding with the most difficult
features in all the varieties of occupation. To-
gether, they satisfy all the demands of the child's
nature in respect both to mental and physical
culture, and lay the surest foundation for all
subsequent education in school and in life.
Th& time of occupation in the Kinder-Garten
is three or four hours on each week day, usually
from 9 to 1 2 or I o'clock ; and the time allot-
ted to each separate occupation, including the
changes from one to another, is from twenty to
thirty minutes. Movement plays, so-called, in
which the children imitate the flying of birds,
swimming of fish, the motions of sowing, mow-
wing, threshing, &c., in connection with light
gymnastics and vocal exercises, alternate with
the plays performed in a sitting posture. All
occupations that can be engaged in out of
doors, are carried on in the garden whenever
the season and weather permit.
For the reason that the various occupations,
as previously stated, are so intimately con-
nected, growing, as it were, out of each other,
they are introduced very gradually, so as to
afford each child ample time to become suffi-
ciently prepared for the next step, without
interfering, however, with the rapid progress
of such as are of a more advanced age, or
endowed with stronger or better developed
faculties.
The following is a list of the gifts or ma-
"terial and means of occupation in the Kinder-
Garten, each of which will be specified and
described separately hereafter.
There are altogether twenty gifts, according
to Froebel's general definition of the term, al-
though the first six only are usually designated
by this name. We choose to follow the classi-
fication and nomenclature of the great inventor
of the system.
LIST OF FROEBEL'S GIFTS.
1. Six rubber balls, covered with a net-work
of twine or worsted of various colors.
2 . Sphere, cube, and cylinder, made of wood.
3. Large cube, consisting of eight small
cubes.
4. Large cube, consisting of eight oblong
parts.
5. Large cube, consisting of whole, half,
and quarter tubes.
6. Large cube, consisting of doubly divided
oblongs.
[The third, fourth, fifth and sixth gifts serve
for building purposes.]
7. Square and triangular tablets for laying
of figures.
GUIDE TO KINDER- GARTNERS.
8. Staffs for laying of figures.
9. Whole and half rings for laying of
figures.
10. Material for drawing.
11. Material for perforating.
12. Material for embroidering.
13. Material for cutting of paper and com-
bining pieces.
14. Material for braiding.
15. Slats for interlacing.
16. The slat with many links.
17. Material for intertwining.
18. Material for paper folding.
19. Material for peas-work.
20. Material for modeling.
THE FIRST GIFT.
The First Gift, which consists of sLx rubber
balls, over-wrought with worsted, for the pur-
pose of representing the three fundamental
and three mLxed colors, is introduced in this
manner:
The children are made to stand in one or
two rows, with heads erect, and feet upon a
given line, or spots marked on tlie floor.
The teacher then gives directions like the
following :
" Lift up your right hands as high as you
can raise them."
" Take them down."
" Lift up your left hands." " Down."
" Lift up both your hands." " Down."
" Stretch forward your right hands, that I
may give each of you something tliat I have
in my box."
The teacher then places a ball in the hand
of each child, and asks —
" Who can tell me the -name of what you
have received ? " Questions may follow about
the color, material, shape, and other qualities
of the ball, which will call forth the replies,
blue, yellow, rubber, round, light, soft, &c.
The children are then required to repeat
sentences pronounced by the teacher, as —
"The ball is round;" ^' My ball is green;"
"All these balls are made of rubber," &c.
They are then required to return all, except
the blue balls, those who give up theirs being
allowed to select from the box a blue ball in
exchange ; so that in the end each child has
a ball of that color. The teacher then says :
" Each of you has now a blue, rubber ball,
which is round, soft,znd light; and these balls
will be your balls to play with. I will give
you another ball to-morrow, and the next day
another, and so on, until you have quite a
number of balls, all of which will be of rub-
ber, but no two of the same color."
The six differently colored balls are to be
used, one on each day of the week, which
assists the children in recollecting the days of
the week, and the colors. After distributing
the balls, the same questions may be asked as
at the beginning, and the children taught to
raise and drop their hands with the balls in
them ; and if there is time, they may make a
few attempts to Uirow and catch the balls.
This is enough for the first lesson ; and it will
be sure to awaken enthusiasm and delight in
die children.
The object of the first occupation is to teach
the children to distinguish between the right
and the left hand, and to name the various
colors. It may serve also to develop their
vocal organs, and instaict them in the rules
of politeness. How the latter may be accom-
plished, even with such simple occupation as
playing with balls, may be seen from the fol-
lowing :
In presenting the balls, pains should be
taken to make each child extend the right
GUIDE TO KINDER-GARTNERS.
hand, and do it gracefully. The teacher, in
putting the ball into the little outstretched
hand, says :
" Charles, I place this red (green, yellow,
&c.,) ball into your right hand." The child
is taught to reply —
" I thank you, sir."
After the play is over, and the balls are to
be replaced, each one says, in returning his
ball—
" I place this red (green, yellow, &c.,) ball,
with my right hand, into the box."
When the children have acquired some
knowledge of the different colors, they may
be asked at the commencement :
" With which ball would you like to play
this morning — the green,, red, or blue one ? "
The child will reply :
" With the blue one, if you please ; " or one
of such other color as may be preferred.
It may appear rather monotonous to some
to have each child repeat the same phrase ;
but it is only by constant repetition and
patient drill that anything can be learned
accurately ; and it is certainly important that
these youthful minds, in their formative state,
should be taught at once the beauty of order
and the necessity of rules. So the left hand
should never be employed when tlie right
hand is required; and all mistakes should
be carefully noticed and corrected by the
teacher. One important feature of this sys-
tem is the inculcation of habits of precision.
The children's knowledge of color may be
improved by asking them what other things
are similar to the different balls, in respect to
color. After naming several objects, they
may be made to repeat sentences like the fol-
lowing :
" My ball is green, like a leaf" " My ball
is yellow, like a lemon." " And mine is red,
like blood," &c.
Whatever is pronounced in these conversa-
tional lessons should be articulated very dis-
tinctly and accurately, so as to develop the
organs of speech, and to correct any defect
of utterance, whether constitutional or the
result of neglect. Opportunities for phonetic
and elocutionary practice are here afforded.
Let no one consider the infant period as too
early for such exercises. If children learn to
speak well before they learn to read, they
never need special instruction in the art of
reading with expression.
For a second play with the balls, the class
forms a circle, after the children have received
the balls in the usual manner. They need to
stand far enough apart, so that each, -with
arms extended, can just touch his neighbor's
hand. Standing in this position, and having
the balls in their right hands, the children
pass them into the left hands of their neigh-
bors. In this way, each one gives and re-
ceives a ball at the same time, and the left
hands should, therefore, be held in such a
manner that the balls can be readily placed
in them. The arms are then raised over the
head, and the balls passed from, the left into
the right hand, and the arms again extended
into the first position. This process is re-
peated until the balls make the complete
circuit, and return into the right hands of the
original owners. The balls are then passed
to the left in the same way, everything being
done in an opposite direction. This exercise
should be continued until it can be 3one
rapidly and, at the same time, gracefully.
Simple as this performance may appear to
those who have never tried it, it is, neverthe-
less, not easily done by very young children
without frequent mistakes and interruptions.
It is better that the children should not turn
their heads, so as to watch their hands during
the changes, but be guided solely by the sense '
of touch ; and to accomplish this with more
certainty, they may be required to close their
eyes. It is advisable not to introduce this
play or any of the following, until expertness
is acquired in the first and simpler form.
In the third play, the children forrii in two
rows fronting each other. Those of one row
only receive balls. These they toss to the
opposite row : first, one by one ; then two by
two; finally, the whole row at once, always
GUIDE TO KINDER-GARTNERS.
to the counting of the teacher — "one, two,
throw."
Again, forming four rows, the children in
the first row toss up and catch", tlien throw to.
the second row, then to the third, then to the
fourth, accompanying the exercise with count-
ing as before, or with singing, as soon as this
can be done.
For a further variety, the balls are thrown
upon the floor, and caught, as they rebound,
with the rig/tt hand or the ic/t hand, or witli
the hand inverted, or they may be sent back
to the floor several times before catching.
Throwing the balls against the wall, tossing
them into the air, and many other exercises
may be introduced whenever the balls are
used, and will always serv-e to interest the
children. Care should be taken to have every
movement performed in perfect order, and that
every child take part in all the exercises in its
turn.
At the close of every ball play, the children
occupy their original places marked on the
floor, the balls are collected by one or two of
the older pupils, and after this has been done,
each child takes the hand of its opposite
neighbor, and bowing, says, " good morning,"
when they march by twos, accompanied by
music, once or twice through the hall, and
then to their seats for other occupation.
THE SECOND GIFT.
The Second Gift consists of a sphere, a
cube, and a cylinder. These the teacher places
upon the table, together with a rubber ball,
and asks :
" Which of these three objects looks most
like theball?"
The children will certainly point out the
sphere, but, of course, without giving its name.
" Of what is it made ?•" the teacher asks,
placing it in the hand of some pupil, or rolling
it across the table.
The answer will doubtless be, " Of wood."
" So we might call the object a wooden ball.
But we will give it another name. We will
call it a sphere."
Each child must here be taught to pro-
nounce the word, enunciating each sound very
distinctly. The ball and sphere are then fur-
ther compared with each other, as to material,
color, weight, &c., to find their similarities
and dissimilarities. Both are round; both
roll. The ball is soft; the sphere is hard.
The ball is light; the sphere is heaiiy. The
sphere makes a louder noise when it falls from
the table than the ball. The ball rebounds
when it is thrown upon the floor ; the sphere
does not. All these answers are drawn out
from the pupils by suitable experiments and
questions, and every one is required to repeat
each sentence when fully explained.
The children then form a circle, and the
teacher rolls the sphere to one of them, ask-
ing the child to stop it with both his feet.
This child then takes his place in the center,
and rolls the sphere to another one, who again
stops it with his feet, and so on, until all the
children have in turn taken their place in the
center of the circle. At another time, the
children may sit in two rows upon the floor,
facing each other. A white and a black
sphere are then given to the heads of the
rows, who exchange by rolling them across to
each other. Then the spheres are rolled
across obliquely to the second individuals in
the rows. These exchange as before, and
then roll the spheres to those who sit third,
and so on, until they have passed throughout
the lines and back again to the head. Both
GUIDE TO KINDER-GARTNERS.
spheres should be rolling at the same instant,
which can be effected only by counting or
when time is kept to accompanying music.
Another variety of play in the use of this
gift consists in placing the rubber ball at a
distance on the floor, and letting each child,
in turn, attempt to hit it with the sphere.
For the purpose of further instruction, the
sphere, cube, and cylinder are again placed
upon the table, and the children are asked
to discover and designate the points of re-
semblance and difference in the first two.
They will find, on examination, that both are
made of wood, and of the same color ; but
the sphere can roll, while the cube cannot..
Inquire the cause for this difference, and the
answer will, most likely, be either, " the sphere
is round," or "the cube has corners."
" How many corners has the cube ? " The
children count them, and reply, " Eight."
" If I put my finger on one of these comers,
and let it glide down to the corner below it,
(thus,) my finger has passed along an edge
of the cube. How many such edges can we
count on this cube? I will let my finger
glide over the edges, one after the other, and
you may count."
"One, two, three, 12."
"Our cube, then, has eight corners, and
twelve edges. I will now show you four cor-
ners and four edges, and say that this part
of the cube, which is contained between these
four corners and four edges, is called a side
of the cube. Count how many sides the cube
has."
" One two, three, four, five, si.x."
" Are these sides all alike, or is one small
and another large ? " " They are all alike."
" Then we may say that our cube has six
sides, all alike, and that each side has four
edges, all alike. Each of these sides of the
cube is called a square.^'
To explain the cylinder, a conversation like
the following may take place. It will be ob-
served that instruction is here given mainly
by comparison, which is, in fact, tlie only
philosophical method.
The sphere, cube, and cylinder are placed
together as before, in the presence of the
children. They readily recognize and name
the first two, but are in doubt about the third,
whether it is a barrel or a wheel. They may
be suffered to indulge their fancy for awhile
in finding a name for it, but are, at last, told
that it is a cyHnda; and are taught to pro-
nounce the word distinctly and accurately.
" What do you see on the cylinder which
you also see on the cube ? " " The cylinder
has two"sides." " Are the sides square, like
those of the cube?" " They are not."
But the cylinder can stand on these sides
just as the cube can. Let us see if it cannot
roll, too, as the sphere does. Yes ! it rolls ;
but not like the- sphere, for it can roll only
_in two ways, while the sphere can roll any
way. So, you see, the sphere, cube, and
cylinder are alike in some respects, and differ-
ent in others. Can you tell me in what re-
spects they are just alike?"
" They are made of wood ; are smooth ;
are of the same color; are heavy; make a
loud noise when they fall on the floor."
These answers must be drawn out by ex-
periments with the objects, and by questions,
logically put, so as to lead to these results as
natural conclusions. The e.xercise may be
continued, if desirable, by asking the children
to name objects which look like the sphere,
cube, or cylinder. The edge of a cube may
also be explained as representing a straight
line. The point where two or three lines or
edges meet is called a corner; the inner
point of a corner is an angle, of which each
side, or square, of the cube has four. To
sum up what has already been taught : The
cube has six sides, or squares, all alike ; eight
corners, and twelve edges ; and each side of
the cube has four edges, all alike ; four cor-
ners, and four angles.
The sphere, cube, and cylinder, when sus-
pended by a double thread, can be made to
rotate around themselves, for the purpose of
showing that the sphere appears the same in
form in whatever manner we look at it ; that
GUIDE TO KINDER-GARTNERS.
the cube, when rotating, (suspended at the
center of one of its sides,) shows the form
of the cyhnder ; and that the cylinder, when
rotating, (suspended at the center of its round
side,) presents the appearance of a sphere.
Thus, there is, as it were, an inner triunity
in these three objects — sphere contained in
cyhnder, and cylinder in cube, the cylinder
forming the mediation between the two others,
or the transition from one to the other. Al-
though the child may not be told, the teacher
may think, in this connection, of the natural
law, according to which the fruit is contained
in the flower, the flower is hidden in the bud.
Suspended at other points, cylinder and
cube present other forms, all of which are
interesting for the children to look at, and can
be made instructive to their young minds, if
accompanied by apt conversation on the part
of the teacher.
THE THIRD GIFT.
This consists of a cube, divided into eight
smaller one-inch cubes.
A prominent desire in the mind of ever)'
child is to divide things, in order to examine
the parts of which they consist. This natural
instinct is observable at a very early period.
The little one tries to change its toy by break-
ing it, desirous of looking at its inside, and is
sadly disappointed in finding itself incapable
of reconstructing the fragments. Froebel's
Third Gift is founded on this observation.
In it the child receives a whole, whose parts
he can easily separate, and put together again
at pleasure. Thus he is able to do that which
he could not in the case of the toys — restore
to its original form that which was broken —
making a perfect whole. And not only this —
he can use the parts also for the construction
of other wholes.
The child's first plaything, or means of
occupation, was the ball. Next came the
sphere, similar to, yet so diflerent from, the
ball. Then followed cube and cylinder, both,
in some points, resembling the sphere, yet
each having its own peculiaritiqg, which dis-
tinguish it from the sphere and ball. The
pupil, in receiving the cube, divisible into
eight smaller cubes, meets with friends, and is
delighted at the multiplicity of the gift. Each
of the eight parts is precisely like the whole,
except in point of size, and the child is im-
mediately struck with this quality of his first
toy for building purposes. By simply looking
at this gift, the pupil receives the ideas of
whole a.nd part — of form and cmnparative size ;
and by dividing the cube, is impressed with
the relation of one part to another in regard
to position rfnd order of movements, thus
learning readily to comprehend the use of
such terms as above, below, before, behind, right,
left, &c., &c.
With this and all the following gifts, we
produce what Froebel zaW^ forms of life, forms
of knotuledge, and forms of beauty.
The first are representations of objects which
actually exist, and which come under our com-
mon observation, as the works of human skill
and art. The second are such as afford in-
struction relative to number, order, proportion,
&c. The third are figures representing only
ideal forms, yet so regularly constructed as to
present perfect models of symmetry and order
in the arrangement of the parts. Thus in the
occupations connected with the use of these
simple building blocks, the child is led into
the living world — there first to take notice of
objects by comparison ; then to learn some-
thing of their properties by induction, and
GUIDE TO KINDER-GARTNERS.
lastly, to gather into his soul a love and desire
for the beautiful by the contemplation of those
forms which are regular and symmetrical.
THE PRESENTATION OF THE THIRD GIFT.
The children having taken their usual seats,
the teacher addresses them as follows :
" To-day, we have something new to play
with."
Opening the package and displaying the
box, he does not at once gratify their curiosity
by showing them what it contains, but com-
mences by asking the question —
" Which one of the three objects we played
with yesterday does this box look like?"
They answer readily, " The cube."
" Describe the box as the cube has been
described, with regard to its sides, edges,
corners, &c."
If this is satisfactorily done, the cover may
then be removed, and the box placed inverted
upon the table. If the box is made of wood,
it is placed upon its cover, wliich, when drawn
out will allow the cubes to stand on the table.
Lifting it up carefully, so that the contents may
remain entire, the teacher asks :
" What do you see now?"
The answer is as before, " A cube."
One of the scholars is told to push it across
the table. In so doing, the parts will be likely
to become separated, and that which was pre-
viously whole will lie before them in fragments.
The children are permitted to examine the
small cubes ; and after each one of them has
had one in his hand, the eight cubes are re-
turned to the teacher, who remarks :
" Children, as we have broken the thing, we
must try to mend it. Let us see if we can put
it together as it was before."
This having been done, the boxes are then
distributed among the children, and they are
practiced in removing the covers, and taking
out the cube without destroying its unity.
They will find it difficult at first, and there
will be many failures. But let them continue
to try until some, at least, have succeeded,
and then proceed to another occupation.
PREPARATION FOR CONSTRUCTING
FORMS.
The surface of the tables is covered with a
net-work of lines, forming squares of One inch.
The spaces allotted to the pupils are separated
from each other by heavy dark lines, and the
centers are marked by some different color.
In these first conversational lessons, the chil-
dren must be taught to point out the right
upper corner of their table space, the left
upper, the right and left lower, the upper and
lower edges, the right and left edges, and the
center. With little staffs, or sticks cut at con-
venient lengths, they may indicate direction,
e. g., by laying them upon the table in a line
from left to right, covering the center of the
space, or extending them from the right upper
to the left lower corner covering the center ;
then from the middle of the upper edge to the
middle of the lower edge, and so on. The
teacher must be careful to use terms that can
be easily comprehended, and avoid changing
them in such a way as to produce any ambigu-
ity in the mind of the child.
Here, as in the more advanced exercises,
everj'thing should be done with a great deal
of precision. The children must understand
that order and regularity in all the perform-
ances are of the utmost importance. The
following will serve as an illustration of the
method : The children having received the
boxes, they are required to place them exactly
in the center of their spaces, so as to cover
four squares. They then take hold of the box
with the left hand, and remove the cover with
the right, placing it by the right upper corner
of the net-work on the table. They next
place the left hand upon the open box, and
reverse it with the right hand, so that the left
is on the table. Drawing it carefully from
beneath, they let the inverted box rest on the
squares in the center. The right hand is used
to raise the bpx carefully from its place, and,
if successful, eight small cubes will stand in
the center of the space, forming one large
cube. Lastly, the box is placed in the cover
at the right Upper corner, and care should
GUIDE TO KINDER-GARTNERS.
be taken that all are arranged in exact posi-
tion.
(If the cubes are enclosed in wooden boxes
with covers to be drawn out at the side, these
manipulations are to be changed accordingly.)
At the close of any play, when the ma-
terials are to be returned to the teacher, the
same minuteness of detail must be observed.
Replacing the box over the cubes, placing
the left hand beneath, and lifting the box with
the right, reversing it, and placing it again
upon the center of the table, then covering
it — these are processes which must be re-
peated many times before the scholar can
acquire such expertness as shall render it
desirable to proceed to the real building occu-
pation.
FORMS OF LIFE.
The boxes being opened as directed, and
the cubes upon the center squares — in each
space — the question is asked :
" How many little cubes are there ? "
" Eight."
" Count them, placing them in a row from
left to right," (or from right to left.)
" What is that.' " " A row of cubes."
It may bear any appropriate name which
the children give it — as "a train of cars," "a-
company of soldiers," " a fence," &c.
" Now count your cubes once more, placing
them one upon another. What have you
there ? "
" An upright row of eight cubes."
"Have you ever seen anything standing
like this upright row of cubes ? "
" A chimney." " A steeple."
" Take down your cubes, and build two
upright rows of them — one square apart.
What have you now ? "
" Two little steeples," or " two chimneys."
Thus, with these eight cubes, many forms of
life can be built under the guidance of the
teacher. It is an important rule in this occu-
pation, that nothing should be rudely destroyed
which has been constructed, but each new form
is to be produced by slight change of the pre-
ceding one.
On Plates I. and II., a number of these are
given. They are designated by Froebel as
follows :
1. Cube, or Kitchen Table.
2. Fire-Place.
3. Grandpa's Chair.
4. Grandpa's and Grandma's Chairs.
5. A Castle, with two towers.
6. A Stronghold.
7. A Wall.
8. A High Wall.
9. Two Columns.
10. A Large Column, with two memorial
stones.
11. Sign-Post.
12. Cross.
13. Two Crosses.
14. Cross, with pedestal.
15. Monument.
16. Sentry-Box.
17. A Well.
18. City Gate.
19. Triumphal Arch.
20. City Gate, with Tower.
21. Church.
22. City Hall.
23. Castle.
24. A Locomotive.
25. A Ruin.
26. Bridge, with Keeper's House.
27. Two Rows of Trees.
28. Two Long Logs of Wood.
29. A Bole.
30. Two Small Logs of Wood.
31. Four Garden Benches.
32. Stairs.
33. Double Ladder.
34. Two Columns on Pedestals.
35. Well-Trough.
36. Bath.
37. A Tunnel.
38. Easy Chair.
39. Bench, with back.
40. Cube.
Several of the names in this list represent
objects which, being more specifically German,
will not be recognized by the children. Ruins,
14
GUIDE TO KINDER-GARTNERS.
castles, sentry-boxes, sign-posts, perhaps they
have never aeen ; but it is easy to tell them
something about these objects which will in-
terest them. They will listen with pleasure
to short stories, narrated by way of explana-
tion, and thus associating the story with the
form, be able, at another time, to reconstruct
the latter while they repeat the former in their
own words. It is not to be expected, how-
ever, that teachers in this country should
adhere closely to the list of Froebel. They
may, with advantage, vary the forms, and, if
they choose, affix other names to those given
upon the plates. It is well sometimes to
adopt such designations as are suggested by
the children themselves. They will be found
to be quite apt in tracing resemblances be-
tween their structures and the objects with
which they are familiar.
In order to make the occupation still more
useful, they should be required also to point
out the dissimilarities existing between the
form and that which it represents.
It is proper to allow the child, at times, to
invent forms, the teacher assisting the fantasy
of the little builder in the work of construct-
ing, and in assigning names to the structure.
When a figure has been found, and named,
the child should be required to take the blocks
apart, and build the same several times in suc-
cession. Older and more advanced scholars
suggest to younger and less abler ones, and
the latter will be found to appreciate such
help.
It is a common observation, that the younger
children in a family develop more rapidly than
the older ones, since the former are assisted
in their mental growth by companionship with
the latter. This benefit of association is seen
more fully in the Kinder-Garten, under the
judicious guidance of a teacher who knows
how to encourage what is right, and check
what is wrong, in the disposition of the chil-
dren.
It should be remarked, in connection with
these directions, that in the use of this and
the succeeding gift it is essential that all the
blocks should be used in the building of each
figure, in order to accustom the child to look
upon things as mutually related. There is
nothing which has not its appointed place,
and each part is needed to constitute the
whole. For example, the well-trough (35)
may be built of six cubes, but the remaining
two should represent two pails with which the
water is conveyed to the trough.
FORMS OF KNOWLEDGE.
These do not represent objects, either real
or ideal. They instruct the pupil concerning
the properties and relations of numbers, by
a particular arranging and grouping of the
blocks. Strictly speaking, the first effort to
count, by laying them on the table one after
another, is to be classed under this head. .
The form thus produced, though varied at
each trial, is one of the forms of knowledge,
and by it the child receives its first lesson in
arithmetic.
Proceeding further, he is taught to add,
always by using the cubes to illustrate the
successive steps. Thus, having placed two
of the blocks at a little distance from each
other on the table, he is caused to repeat,
" One and one are two." Then placing
another upon the table, he repeats, " One
and two are three," and so on, until all the
blocks are added.
Subtraction is taught in a similar manner.
Having placed all the cubes upon the table,
the scholar commences taking them off, one
at a time, repeating, as he does this, " One
from eight leaves seven; "One from seven
leaves six," and so on.
According to circumstances, of which the
Kinder-Gartner, of course, will be the best
judge, these exercises may be continued fur-
ther, by adding and subtracting two, three,
and so on ; but care should always be taken
that no new step be made until all that has
j gone before is perfectly understood.
With the more advanced classes, exercises
in multiplication and division may be tried,
by grouping the blocks.
GUIDE TO KINDER-GARTNERS.
15
The division of the large cube, to illustrate
the principles of proportion, is an interesting
and instructive occupation ; and we will here
proceed to give the method in detail.
The children have their cube of eight be-
fore them on the table. The teacher is also
furnished with one, and lifting the upper half
in the manner shown on Plate III., No. 4,
asks:
" Did I take the whole of my cube in my
hand, or did I leave some of it on the table ? "
" Yoii left some on the table."
" Do I hold in my hand more of my cube
than I left on the table, or are both parts
alike .' "
" Both are alike."
" If things are alike, we call them equal.
So I divided my cube into two equal parts,
and each of these equal parts I call a half.
Where are the two halves of my cube ? "
" One is in your hand ; the other is on the
table."
" So I have two half cubes. I will now
place the half which I have in my hand upon
the half standing on the table. What have I
now ? "
" A whole cube."
The teaclier, then separating the cube again
into halves, by drawing four of the smaller
cubes to the right and four to the left, as is
indicated on Plate III., No. 2, asks :
" What have I now before me ? "
" Two half cubes."
" Before, I had an upper and a lower half.
Now, I have a right and a left half. Uniting
the halves again I have once more a whole."
The scholars are taught to repeat as fol-
lows while the teacher divides and unites the
cubes in both ways, and also as represented
by Form No. 3 :
" One whole — two halves."
"Two halves — one whole."
Again, each half is divided, as shown in
Forms No. 5, 6, and 7. and the children are
required to repeat during these occupations :
" One whole — two halves."
"One half — two quarters (or fourths.)"
"Two quarters — one half."
"Two halves — one whole."
After these processes are fully explained,
and the principles well understood by the
scholars, they are to try their hand at divid-
ing of the cube — first, individually, then all
together. If they succeed, they may then be
taught to separate it into eighths. It is not
advisable, in all cases, to proceed thus far.
Children under four years of age should be
restricted, for the most part, to the use of the
cubes for practical building purposes, and for
simpler forms of knowledge.
FORMS OF BEAUTY.
Starting with a few simple arrangements,
or positions, of the blocks, we are able to
develop the forms contained in this class by
means of a fixed law, viz., that every change
of position is to be accompanied by a cor-
responding movement on the opposite side.
In this way symmetrical figures are construct-
ed in infinite variety, representing no real
objects, yet, by their regularity of outline,
adapted to please the eye, and minister to a
correct artistic taste. The love of the beau-
tiful cannot fail to be awakened in the youth-
ful mind by such an occupation as this, and
with this emotion will be associated, to some
extent, the love of the good, for they are in-
separable.
The works of God are characterized by
perfect order and symmetry, and his good-
ness is commensurate with the beauty mani-
fest everj-where in the fruits of his creative
power. The construction of forms of beauty
with the building blocks will prepare the child
to appreciate, by and by, the order that rules
the universe.
By Plates IV. and V. it will be seen that
these forms are of only one block's height,
and, consequently, represent outlines of sur-
faces. It is necessarj' that the children should
be guided, in their construction, by an easily
recognizable center. Around this visible point
all the separate parts of the form to be created
must be arranged, just as in working out the
i6
GUIDE TO KINDER-GARTNERS.
highest destiny of man, all his thoughts and
acts need to be regulated by an invisible cen-
ter, around which he is to construct a har-
monious and beautiful whole.
In order to produce the varied forms of
beauty with the simple material placed in the
hands of the scholar, he must first learn in'
what ways two cubes may be brought in con-
tact with each other. Four positions are
shown on Plate IV. The blocks may be ar-
ranged either — side by side, as in Fig. i ; edge
to edge, as in Fig. 2 ; or edge to side, and side
to edge, as in Nos. 3 and 4. Nos. i and 3 are
the opposites to 2 and 4. Other changes of
position may be made. For example, in Fig. i
the block marked a may be placed above or to
the right or to the left of the block marked b.
The cubes may also be placed in certain rela-
tions to each other on the table, without being
in actual contact. These positions should be
practiced perseveringly at the outset, so as to
furnish a foundation for the processes of con-
struction which are to follow. It is one of the
important features of Froebel's system, that it
enables the child readily to discover, and
critically to observe, all relations which ob-
jects sustain to one another. Thoroughness,
therefore, is required in all the details of these
occupations.
We start from any fundamental form that
may present itself to our mind. Take, for
illustration, Form No. 5. Four cubes are
here united side to side, constituting a square
surface, and the outline is completed by plac-
ing the four remaining cubes severally side to
side with this middle square. In 6, edge
touches edge ; in 7, side touches edge, and in
8, edge touches side midway. Another mode
of development is shown in Forms 9 — 15.
The four outside cubes move toward the
right by a half cube's length, until the original
form reappears in No. 15.
Now, the four outside cubes occupy the
opposite position. Fig. 16, edges touch sides.
They are moved as before, by a half cube's
length, until, in Form No. 22, the one with
which we started, is regained.
We now extract the inside cubes (^), Fig.
23, and each of them travels around its neigh-
bor cube (a), until a standing, hollow square
is developed, as in Fig. 29.
Now cube a again is set in motion. It
assumes a slanting direction to the remain-
ing cubes. Fig. 30, and, pursuing its course
around them, the Form, No. 29, reappears
in No. 36.
Next, b is drawn out. Fig. 37, and a pushed
in, until a standing cross is formed. Fig. 38,
b, constantly traveling on by a half cube's
length, until. Fig. 43, all cubes are united in a
large square, and b again begins traveling, by
a cube's length, turning side to side and edge
to edge. In Fig. 48, b performs as a has
done.
But with more developed children we may
proceed on other principles, Fig. 49, intro-
ducing changes only on two instead of four
sides, and thus arriving successively at Forms
50 — 60.
After each occupation, the scholars should
replace their cubes in the boxes, as heretofore
described, and the material should be re-
turned to the closet where it is kept before
commencing any other play.
THE FOURTH GIFT.
The preceding gift consisted of cubical
blocks, all of their three dimensions being the
same. In the Fourth Gift, we have greater
variety for purposes of construction, since each
of the parts of the large cube is an oblong,
whose length is twice its width, and four times
its thickness. The dimensions bear the same
proportion to each other as those of an or-
dinary brick ; and hence these blocks are
sometimes called bricks. . They are useful in
teaching the child difference in regard to
length, breadth, and height. This difference
enables them to construct a greater variety
of forms than he could by means of the third
gift. By these he is made to understand,
more distinctl)', the meaning of the terms per-
pendicular and horizontal. And if the teacher
sees fit to pursue the course of experiment
sufficiently far, many philosophical truths will
be developed ; as. for instance, the law of
equilibrium, shown by laying one block across
another, or the phenomenon of continuous
motion, exhibited in the movement of a row
of the blocks, set on end, and gently pushed
from one direction.
PREPARATION FOR CONSTRUCTING
FORMS.
This gift is introduced to the children in a
manner similar to the presentation of the third
gift. The cover is removed, and the box is
reversed upon the table. Lifting the box
carefully, the cube remains entire. The chil-
dren are made to observe that, when whole,
its size is the same as that of the previous one.
Its parts, however, are very different in form,
though their number is the same. There are
still eight blocks. Let the scholars compare
one of the small cubes of the third gift with
one of the oblongs in this gift ; note the simi-
3
larities and the differences ; then, if they can
comprehend that notwithstanding they are so
unlike m /arm. their solid contents is the same,
since it takes just eight of each to make the
same sized cube, an important lesson will
have been learned. If told to name objects
that resemble the oblong, they will readily
designate a brkk^ table, piano, closet, &c., and
if allowed to invent forms of life, will, doubt-
less, construct boxes, benches, &c.
The same precision should be observed in
all the details of opening and closing the
plays with this gift as in those previously de-
scribed.
FORMS OF LIFE.
The following is a list of Froebel's forms,
which are represented on Plates VI. and VII.
If the names do not appear quite striking, or
to the point, the teacher may try to substitute
better ones :
1. The Cube.
2. Part of a Floor, or Top of a Table.
3. Two Large Boards.
4. Four Small Boards.
5. Eight Building Blocks.
6. A Long Garden Wall.
7. A City Gate.
8. Another City Gate.
9. A Bee Stand.
10. A Colonnade.
11. A Passage.
12. Bell Tower.
13. Open Garden House.
14. Garden House, with Doors.
15. Shaft.
16. Shaft.
17. A Well, with Cover.
18. Fountain.
19. Closed Garden Wall.
18
GUIDE TO KINDER-GARTNERS.
20. An Open Garden.
21. An Open Garden.
22. Watering-Trough.
23. Shooting-Stand.
24. Village.
25. Triumphal Arch.
26. Caroussel.
27. Writing Desk.
28. Double Settee.
29. Sofa.
30. Large Garden Settee.
31. Two Chairs.
32. Garden Table Chairs.
33. Children's Table.
34. Tombstone.
35. Tombstone.
36. Tombstone.
37. Monument.
38. Monument.
39. Winding Stairs.
40. Broader Stairs.
41. Stalls.
42. A Cross Road.
43. Tunnel.
44. Pyramid.
45. Shooting-Stand.
46. Front of a House.
47. Chair, with Footstool.
48. A Throne.
49. f Illustration of
50. \ Continuous Motion.
Here, as in the use of tlie previous gift,
one form is produced from another by slight
changes, accompanied by explanations on the
part of the teacher. Thus, Form 30 is easily
changed to 31, 32, and ^3, and Form 34 may
be changed to 35, 36, and 37. In every case,
all the blocks are to be employed in con-
structing a figure.
FORMS OF KNOWLEDGE.
This gift, like the preceding, is used to
communicate ideas of divisibility. Here, how-
ever, on account of the particular form of
the parts, the processes are adapted rather to
illustrate the division of a surface, than of a
solid body.
The cube is first arranged so that one per-
pendicular and three horizontal cuts appear,
aiid a child is then requested to separate it into
halves, these halves into quarters, and these
quarters into eighths. Each of the latter will
be found to be one of the oblong blocks, and
this for the time, may be made the subject of
conversation.
" Of what material is this block made ? "
"What is the color?"-
"What objects resemble it in form?"
" How many sides has it?"
" Which is the largest side ? "
"Which is the smallest side?"
" Is there a side larger than the smallest
and smaller than the largest?"
In this way, the scholars learn that there
are three kinds of sides, symmetrically arrang-
ed in pairs. The upper and lower, the right
and left, the front and back, are respectively
equal to and like each other.
By questions, or by direct explanation, facts
like the following, may be made apparent to
the minds of children. "The upper and low-
er sides of the block are twice as large as the
two long sides, or the front and back, as they
may be called. Again, the front and back are
twice as large as the right and left, or the two
short sides of the block. Consequently, the
two largest sides are four times as large as
the two smallest sides." This can be demon-
strated in a very interesting way, by placing
several of the blocks side by side, in a varie-
ty of positions, and in all these operations
the children should be allowed to experiment
for themselves. The small cubes of the pre-
ceding gift may also with propriety be brought
in comparison with the oblongs of this gift, and
the differences observed.
When the single block has been employed
to advantage, through several lessons, the
whole cube may then be made use of, for the
representation of forms of knowledge.
Construct a tablet or plane as in Plate VIII.
a. In order to show the relations of dimen-
sion, divide this plane into halves, either by a
perpendicular or horizontal cut (b and c).
GUIDE TO KINDER-GARTNERS.
19
These two forms will give rise to instruct-
ive observations and remarks by asking :
" What was the form of the original tablet?"
"What is the form of its halves? "
" How many times larger is their breadth
than their height ? "
So with regard to the position of the oblong
halves ; the one at b may be said to be lying
while that at c is statiding.
" Change a lying to a standing oblong." In
order to do this, the child will move the first
so as to describe a quarter of a circle to the
right or left.
"Unite two oblongs by joining their small
sides. You then have a large lying oblong "(f).
"Separate again (/) and divide each part
into halves, (;'). You have now four parts
called quarters, and these are squares, in their
surface form."
Each of these quarters may be subdivided,
and the children taught the method of division
by two. Other material may also be used in
connection with the blocks, such as apples, or
any small objects which serve to illustrate the
properties of number. It is evident that these
operations should be conducted in the most
natural way, and never begun at too early a
stage of development of the little ones. In
figures e, g, h and k on Plate VIII. another
mode is indicated, for the purpose of illus-
trating further the conditions of form connect-
ed with this gift. Figs, i— 16 Plate VIII.
show the manner in which exercises in addition
and subtraction may be introduced, as has al-
ready been alluded to in the description of the
Third Gift.
FORMS OF BEAUTY.
We first ascertain, as in the case of the
cubes, the various modes in which the oblongs
can be brought in relation to each other.
These are much more numerous than in the
Third Gift, because of the greater variety in
the dimensions of the parts. Plate IX. shows
a number of forms of beauty derivable from
the original form, I. Each two blocks form
a separate group, which four groups touching
in the center, form a large square. The out-
side blocks (a) move in Figs, i — 9, around the
stationary middle.
The inside blocks {b) are now drawn out
(Fig. 10), then the blocks (a) united to form
a hollow square (Fig. 11), around which b
moves gradually (Figs. 12 and 13).
Now b is combined into a cross with open
center, a goes out (Fig. 14) and moves in an
opposite direction until Fig. 17 appears.
By extricating b the eight-rayed star (Fig.
18) is formed. In Fig. 19 a revolves, b is
drawn out until edge touches edge, and thus
the form of a flower appears (Fig. 20).
Now b is turned (Fig. 21), and in Fig. 22,
a wreath is shown. In Fig. 22, the inside
edges touch each other; in Fig. 23, inside
and outside ; in Fig. 24, edges with sides, and
b is united to a large hollow square, around
which a commences a regular moving. In
Fig. 29, a is finally united to a lying cross, and
thereby another starting-point gained for a
new series of developments.
Each of these figures can be subjected to
a variety of changes by simply placing the
blocks on their long or short sides, or as the
children will say, by letting them stand up or
lie down. The net-work of lines on the
table is to be the constant guide, in the con-
struction of forms. In inventing a new series,
place a block above, below, at the right or
left of the center ; and a second opposite and
equidistant. A third and a fourth are placed
at the right and left of these, but in the same
position relative to the center. The remain-
ing four are placed symmetrically about those
first laid. By moving the a's or Vf, regularly
in either direction, a variety of figures may
be formed.
THE FIFTH GIFT.
CUBE, TWICE DIVIDED IN EACH DIRECTION.
(plates X. .TO XVI.)
All gifts used as occupation material in the
Kinder-Garten develop, as previously stated,
one from another. The Fifth Gift, like that
of the Third and Fourth Gifts, consists of a
cube again, although larger than the previous
ones. The cube of the Third Gift was divided
mice in all directions. The natural progress
from I is to 2 ; hence the cube of the Fifth
Gift is divided twict in all directions ; conse-
quently, in three equal parts, each consisting
of 7iine smaller cubes of equal size. But as
this division would only have multiplied, not
diversified, the occupation material, it was
necessary to introduce a new element, by
subdividing some of the cubes in a slanting
direction.
We have heretofore introduced only perpen-
dicular and horizontal lines. These opposites,
however, require their mediate element, and
this mediation was already indicated in the
forms of life and of beauty of the Third and
Fourth Gifts, when side and edge, or edge
and side, were brought to touch each other.
The slanting direction appearing there trans-
itionally — occasionally — here, becomes per-
manent by introducing the slanting line, sepa-
rated by the division of the body, as a bodily
reality.
Three of the part cubes of the Fifth Gift
are divided into half cubes, three others into
quarter cubes, so that there are left twenty-
one whole cubes of the twenty-seven, produced
by the division of the cube mentioned before,
and the whole Gift consists of thirty-nine sin-
gle pieces.
4
It is most convenient to pack them in the
box, so as to have all half and quarter cubes
and three whole cubes in the bottom row, (see
Plate XV., 1%) which only admits of separating
the whole cube in the various ways required
hereafter, as it will also assist in placing the
cube upon the table, which is done in the
same manner as described with the previous
Gifts.
The first practice with this Gift is like that
with others introduced thus far. Led by the
question of the teacher, the pupils state that
this cube is larger than their other cubes;
and the manner in which it is divided will
next attract their attention. They state how
many times the cube is divided in each "direc-
tion, how many parts we have if we separate
it according to these various divisions, and
carrying out what we say, gives them the
necessary assistance for answering these ques-
tions correcdy. In No. 3, Plate XV., the three
parts of the cube have been laid side by side
of each other.
These three squares we can again divide
in three parts, and these latter again in three,
so that then we shall have twenty-seven parts,
which teaches the pupil that 3X3=9-3X9
= 27.
To some, the repetition of the apparently
simple e-xercises may appear superfluous ; but
repetition alone, in this simple manner, will
assist children to remember, and it is always
interesting, as they have not to deal with ab-
stractions, but have real things to look at for
the formation of their conclusions.
GUIDE TO KINDER-GARTNERS.
But, again I say, do not continue these
occupations any longer than you can com-
mand the attention of your pupils by them.
As soon as signs of fatigue or lackof interest
become manifest, drop the subject at once,
and leave the Gift to the pupils for their own
amusement. If you act according to this ad-
vice, your pupils never will over-e.xert them-
selves, and will always come with enlivened
interest to the same occupation whenever it
is again taken up.
After the children have become acquainted
with the manner of division of their new
large cube, and have exercised with it in the
above-mentioned way, their attention is drawn
to the shape of the divided half and quarter
cubes.
They are divided by means of slanting lines,
which should be made particularly prominent,
and the pupils are then asked to point out,
on the whole cubes, in what manner they
were divided in order to form half and quar-
ter cubes. The pupils also point out hori-
zontal, perpendicular and slanting lines which
they observe in things in the room or other
near objects.
Take the two halves of your cube apart,
and say, " How many corners and angles you
can count on the upper and lower sides of
these two half cubes?" "Three." Three
corners and three angles, which latter, you
recollect, are the insides of corners. We call,
therefore, the upper and lower side of the
half cube a triangle, which simply means a
side or plane with three angles. The child
has now enriched its knowledge of lines by
the introduction of the oblique or slanting
line, in addition to the horizontal and perpen-
dicular lines, and of sides or planes by the
introduction of the triangle, in addition to
the square and oblong previously introduced.
With the introduction of the triangle, a great
treasure for the development of forms is
added, on account of its frequent occurrence
as elementary forms in all the many forma-
tions of Tegular objects.
The child is expected to know this Gift now
sufficiently to employ it for the production
of the various forms of life and beauty now
to be introduced.
FORMS OF LIFE.
(plates X. AND XI.)
The main condition here, as always, is
that for each representation the whole of
the occupation material be employed; not
that only one object should always be built,
but in such manner that remaining pieces
be always used to represent accessory parts,
although apart from, yet in a certain rela-
tion to the main figure. The child should,
again and again, be reminded that nothing
belonging to a whole is, or could be, allowed
to be superfluous, but that each individual
part is destined to fill its position actively
and effectively in its relation to some greater
whole.
Nor should it be forgotten that nothing
should be destroyed, but everything produced
by re-building. It is advisable always to start
with the figure of the cube.
There are only the few following models on
our Plates lo and ii :
1. Cube.
2. Flower-Stand.
3. Large Chair.
4. Easy Chair, with Foot Bench.
5. A Bed. Lowesfrow, fifteen whole cubes ;
second row, six whole and six half cubes, com-
posed of twelve quarter cubes; third row, six
half cubes.
6. Sofa. First row, sixteen whole and two
half cubes ; 6°, ground plan.
7. A Well. 7°, ground plan.
8. House, with Yard. 8% ground plan ;
twelve wTiole cubes, ground ; nine whole and
six half cubes, second row ; roof, twelve quar-
ter cubes.
9. A Peasant's House. First row, ten
whole cubes ; second row, eight whole and
two half cubes; roof, eight cubes, three
halves and two halves, and eight quarters
and two halves and four quarters ; 9°, ground
plan.
GUIDE TO KINDER-GARTNERS.
23
10. School-House. Third row, three whole
and six half cubes; fourth row, one whole
and four quarter cubes ; 10°, ground plan.
11. Church. Building itself. eighteen whole
cubes ; roof, twelve quarter cubes ; steeple,
four whole cubes and one half cube ; vestry,
one whole and one half cube ; 1 1°, ground
plan of Church.
12. Church, with Two Steeples. Building
itself, twelve whole cubes ; roof, twelve quar-
ter cubes ; steeples, twice five whole cubes
and one half cube ; between steeples, one
whole cube ; 12", ground plan.
13. Factory, with Chimney and Boiler-
house. Factory, sixteen whole cubes; roof,
six half and four quarter cubes ; chimney, five
whole and two quarter cubes ; boiler-house,
four quarter cubes ; roof, two quarter cubes ;
13", ground plan.
14. Chapel, with Hermitage.
15. Two Garden Houses, with Rows of
Trees.
16. A Castle. 16", ground plan.
17. Cloister in Ruins. 17°, ground plan.
18. City Gate, with Three Entrances. 18°,
ground plan.
19. Arsenal. 19°, ground plan.
20. City Gate, with Two Guard-Houses.
20°, ground plan.
21. A Monument. 21°, ground plan; first
row, nine whole and four half cubes ; second
to fourth row, each, four whole cubes ; on
either side, two quarter cubes, united to a
square column, and to unite the four columns,
four quarter cubes.
22. A Monument. 22°, ground plan; first
row, nine whole and four quarter cubes ; sec-
ond row, five whole and four half cubes ; third
row, four whole cubes ; fourth row, four half
cubes.
23. A Large Cross. 23°, ground plan ; first
row, nine whole and four times three quarter
cubes ; second row, four whole cubes ; third
row, four half cubes.
Tables, chairs, sofas, beds, arc the first
objects the child builds. They are the ob-
jects with which it is most familiar. Then
the child builds a house, in which it lives,
speaking of kitchen, sleeping-room, parlor,
and eating-room, when representing it. Soon
the realm of its ideas widens. It roves into
garden, street, &c. It builds the church, the
school-house, where the older brothers and
sisters are instructed ; the factory, arsenal,
from which, at nooii and after the day's work
is over, so many laborers walk out to their
homes, to eat their dinner and supper, to
rest from their work, and to play with their
little children. The ideas which the children
receive of all these objects by this occupa-
tion, grow more correct by studying them in
their details, where they meet with them in
reality. In all this they are, as a matter
of course, to be assisted by the instructive
conversation of the teacher. It is not to be
forgotten that the teacher may influence the
minds of the children veiy favorably, by re-
lating short stories about things and persons
in connection with the object represented.
Not their minds alone are to be -disciplined ;
their hearts are to be developed, and each
beautiful and noble feeling encouraged and
strengthened.
Be it remembered again that it is not neces-
sary that the teacher should always follow the
course of development shown in the pictures
on our plates. Every course is acceptable,
if only destruction is prevented and re-build-
ing adhered to. Some of the pictures may
not be familiar to some of the children. The
one- has never seen a castle or a city gate,
a well or a monument. Short descriptive
stories about such objects will introduce the
child into a new sphere of ideas, and stimu-
late the desire to see and hear more and
more, thus adding, daily and hourly, to the
stock of knowledge of which he is already
possessed. Thus, these plays will not only
cultivate the manutil dexterity of the child,
develop his eye, excite his fantasy, strengthen
his power of invention, but the accompanying
oral illustrations will also instruct him, and
create in him a love for the good, the noble,
the beautiful.
24
GUIDE TO KINDER-GARTNERS.
The Fifth Gift is used with children from
five to six years old, who are expected to be
in their third year in the Kinder-Garten.
A box, with its contents, stands on the
table before each child. They empty the
box, as heretofore described, so that the bot-
tom row of the cube, containing the half and
quarter cubes, is made the top row.
" What have you now ? "
" A cube."
" We will build a church. Take off all
quarter and half cubes, and place them on
the table before you in good order. Move
the three whole cubes of the upper row
together, so that they are all to the left of
the other cubes. Take three more whole
cubes from the right side, and put them be-
side the three cubes which were left of the
upper row. Take the three remaining cubes,
which were on the right side, and add them
to the quarter and half cubes. What have
you now ? "
" A house without roof, three cubes high,
three cubes long, and two cubes broad."
" We will now make the roof Place on
each of the six upper cubes a quarter cube
with its largest side. Fill up the space be-
tween each two quarter cubes with another
quarter cube, and place another quarter cube
on top of it. What have you now ? "
" A house with roof."
" How many cubes are yet remaining .? "
" Three whole and six half cubes."
" Take the whole cubes, and place them,
one on top of the other, before the house.
Add another cube, made of two half cubes,
and cover the top with half a cube for a roof.
What have you now .'' "
" A steeple."
'• We will employ the remaining three half
cubes to build the entrance. Take two of the
half cubes, form a whole cube of them, and
place it on the other side of the house, op-
posite the steeple, and lay upon it the last
half cube as a roof. What have we built
now ? "
" A cliurch, with steeple and entrance."
FORMS OF BEAUTY.
If we consider that the Fifth Gift is put
into the hands of pupils when they have
reached the fifth year, with whom, conse-
quently, if they have been treated rationally,
the external organs, the limbs, as well as the
senses, and the bodily mediators of all men-
tal activity, the nerves, and their central organ,
the brain, have reached a higher degree of
development, and their physical powers have
kept pace with such development, we may
well expect a somewhat more extensive activ-
ity of the pupils so prepared, and be justified
in presenting to them work requiring more
skill and ingenuity than that of the previous
Gifts.
And, in fact, the progress with these forms
is apparently much greater than with the
forms of life ; because here the importance
of each of the thirty-nine parts of the cube
can be made more prominent. He who is
not a stranger in mathematics knows that the
number of combinations and permutations of
thirty-nine different bodies does not count by
hundreds, nor can be expressed by thousands;
but that millions hardly suffice to exhaust all
possible combinations.
Limitations are, therefore, necessary here ;
and these limitations are presented to us in
tiie laws of beauty, according to which the
whole structure is not only to be formed har-
moniously in itself, but each main part of it
mast also answer the claims of symmetry.
In order to comply with these conditions, it
is sometimes necessary, during the process
of building a Form of Beauty, to perform
certain movements with various parts simul-
taneously. In such cases it appears advis-
able to divide the activity in its single parts,
and allow the child's eye to rest on these
transition figures, that it may become perfectly
conscious of all changes and phases during
the process of development of the form in
question. This will render more intelligible
to the young mind, that real beauty can only
be produced when one opposite balances
another, if the proportions of all parts are
GUIDE TO KINDER-GARTNERS.
25
equally regulated by uniting them with one
common center.
Another limitation we find in the fact, that
each fundamental form from which we start
is divided in two main parts — the internal
and the external— and that if we begin the
changes or mutations with one of these oppo-
sites, they are to be continued with it until a
certain aim be reached. By this process cer-
tain small series of building steps are created,
which enable the child — and, still more, the
teacher — to control the method according to
which the perfect form is reached.
" Each definite beginning conditions a cer-
tain process of its own, and however much
liberty in regard to changes may be allowed,
they are always to be introduced within cer-
tain limils only."
Thus, tlie fundamental form conditions all
the changes of the whole following series.
All fundamental forms are distinct from each
other by their different centers, which may be
a square, (Plate XII., Fig. 9,) a triangle,
(Plate XIV., Fig. 37,) a he.xagon, octagon, or
circle.
Before the real formation of figures com-
mences, the child should become acquainted
with the combinations in which the new forms
of the divided cubes can be brought with
each other. It takes two half cubes, forms
of them a whole, and, being guided by the
law of opposites, arrives at the forms repre-
sented on Plate XII. — i to 8, and perhaps at
others of less significance.
The scries of figures on Plates XIIL, XIV.,
XV., arc all developed, one from another, as
the careful observer will easily detect. As it
would lead too far to show the gradual grow-
ing of one from another, and all from a com-
mon fundamental form, we will show only the
course of development of Figures 9 to 14, on
Plate XII.
The fundamental form (Fig. 9) is a stand-
ing square, formed of nine cubes, and sur-
rounded by four equilateral triangles.
The course of development starts from the
center part. The four cubes a move exter-
nally, (Fig. 10,) the four cubes li do the same,
(Fig. II,) cubes a move farther to the corner
of the triangles, (Fig. 12,) cubes i move to
the places where cubes a were previously,
(Fig. 13.) If all eight cubes continue their
way in the same manner, we ne.xt obtain a
form in which a and l> remain with their cor-
ners on the half of the catheti ; then follows
a figure like 13, different only in so far as a
and -i^ have exchanged positions; then, in
like manner, follow 12, 11, 10, and 9.
We, therefore, discontinue the course. The
internal cubes so far occupied positions that
l> and iT turned corners, a and c sides towards
each other. In Fig. 14, the opposite appears,
/> and t: show each other sides, a and £ cor-
ners. Thus, in Fig. 15, we reach a new
fundamental form. Here, not the cubes of
the internal, but those of the external tri-
angles furnish the material for changing the
form.
It is not necessaiy that the teacher, by
strictly adhering to the law of development,
return to the adopted fundamental form. She
may interrupt the course, as we have done,
and continue according to new conditions.
But however useful it may be to leave free
scope to the child's own fantasy, we should
never lose sight of Froebel's principle, to lead
to Imnful action, to accustom to following a
definite rule. Nor should we ever forget that
the child can only derive benefit from its
occupation, if we do not over-tax the measure
of its strength and ability. The laws of for-
mation should, therefore, always be as definite
and distinct as simple. As soon as the child
cannot trace back the way in which you have
led it, in developing any of the forms of life
or beauty ; if it cannot discover how it arrived
at a certain point, or how to proceed from it,
the moment has arrived when the occupation
not only ceases to be useful, but commences
to be hurtful, and we should always studiously
avoid that moment.
In order to facilitate the child's control of
his activity, it is well to give the cubes, which
arc, so to say, the representatives of the law
26
GUIDE TO KINDER-GARTNERS.
of development, instead of the letters a, b, c,
names of some children present, or of friends
of the pupils. This enlivens the interest in
their movements, and the children follow them
with much more attention.
FORMS OF KNOWLEDGE.
(plates XV. AND XVI.)
The representations of the forms of knowl-
edge, to which the Fifth Gift offers oppor-
tunity, is of great advantage for the develop-
ment of the child. To superficial observers,
it is true, it may appear as if Froebel not
only ascribed too much importance to the
mathematical . element to the disadvantage
of others, but that mathematics necessarily
require a greater maturity of understanding
than could be found with children of the
Kinder-Garten age. But who thinks of in-
troducing mathematics as a science ? Many
a child, five or six years of age, has heard
that the moon revolves around the earth, that
a locomotive is propelled by steam, and that
lightning is the effect of electricity. These
astronomical, dynamic and physical facts have
been presented to him, as mathematical facts
are presented to his observation in Froebel's
Gifts. Most assuredly it would be folly, if one
would introduce in the Kinder-Garten math-
ematical problems in the usual abstract man-
ner. In the KinderGarten, the child beholds
the bodily representation of an expressed
truth, recognizes the same, receives it without
difficulty, without overtaxing its developing
mind in any manner whatsoever. Whatever
would be difficult for the child to derive from
the mere word, nay, which might under cer-
tain circumstances be hurtful to the young
mind, is taught naturally and in an easy man-
ner by the forms of knowledge, which thus
become the best means of e-xercising the
child's power of observation, reasoning, and
judging. Beware of all problems and ab-
stractions. The child builds, forms, sees,
observes, compares, and then expresses the
truth it has ascertained. By repetition, these
truths, acquired by the observation of facts.
become the child's mental property, and this
is not to be done hurriedly, but during tlie
last two years in the Kinder-Garten and
afterwards in the Primary Department.
The first seven forms of knowledge on
Plate XV. show the regular divisions of the
cube in three, nine and twentj'-seven parts,
lu cither case, a whole cube was employed,
and yet the forms produced by division are
different. This shows that the contents may
be equal, when forms are different (Figs. 2, 3,
4, or 5 and 6).
This difference becomes still more obvious
if the three parts of Fig. 2, are united to a
standing oblong, or those of Fig. 3 to a lying
oblong, or if a single long beam is formed of
Fig. 4.
Take a cube, children, place it bc'fore you,
and also a cube divided in two halves, and
place the two halves with their triangular
planes or sides, one upon another.
These two halves united are just as large
as the whole cube.
But the two halves may be united, also, in
other ways. They may touch each other with
their quadratic and right angular planes.
Represent these different ways of uniting
the two halves of the cube simultaneously.
Notwithstanding the difference in the forms,
the contents of mass of matter remained the
same.
In a still more multiform manner, this fact
may be illustrated with the cubes divided in
four parts. Similar exercises follow now with
the whole Gift, and the children are led to
find out all possible divisions in two, three,
four, five, nine and twelve equal parts (Figs.
8 to 18).
After each such division the equal parts
are to be placed one upon another, for divid-
ing and separating are always to be followed
by a process of combining and re-uniting.
The child thus receives every time, a trans-
formation of the whole cube, representing the
same amount of matter in various forms
(Fig. 19-22). The child should also be al-
lowed to compare with each other the various
GUIDE TO KINDER-GARTNERS.
27
thirds, quarters, or sixths, into which whole
cubes can be divided, as shown in Figs. 9,
10, II, 12, or 14, 15 and 16.
It is understood that all these exercises
should be accompanied by the living word
of the teacher ; for thereby, only, will the
child become perfectly conscious of the ideas
received from perception, and the opportunity
is offered to perfect and multiply them. The
teacher should, however, be carefuF not to
speak too much, for it is only necessary to
keep the attention of the pupil to the object
represented, and to render impressions more
vivid.
The divisions introduced heretofore, are
followed by representations of regular mathe-
matical figures, (planes,) as shown in Figs.
23-26. The manner in which one is formed
from the preceding one is easily seen from
the figures themselves.
As mentioned before, part of the occupa-
tion described in the preceding pages, is to
be introduced in the Primary Department
only, where it is combined with other inter-
esting but more complicated exercises. Sim-
ply to indicate how advantageously this Gift
may be used for instruction in geometiy in
later years, we have added the Figs. 30" and
30'', the representation of which shows the
child the visible proof of the well-known
Pythagorean axiom, by which the theoretical,
abstract solution of the same, certainly, can
alone be facilitated.
For the continuation of the exercises in
arithmetic, begun with the previous Gifts, the
cubes of the present one are of great use.
Exercises in addition and subtraction are con-
tinued more extensively, and by the use of
these means, the child will be enabled to
learn, what is usually called the multiplication
table, in a much shorter time and in a much
more rational way than it could ever be ac-
complished by mere memorizing, without visi-
ble objects.
THE SIXTH GIFT.
LARGE CUBE, CONSISTING OF DOUBLY DIVIDED OBLONGS.
(plates XVII. TO XX.)
As the Third and Fifth Gifts form an
especial sequence of development, so the
Fourth and Sixth are intimately connected
with each other. The latter is, so to say, a
higher potence of the former, permitting, the
observation in greater clearness, of the quali-
ties, relations, and laws, introduced previously.
The Gift contains twenty-seven oblong
blocks or bricks, of the same dimensions as
those of the Fourth Gift. Of these twenty-
seven blocks, eighteen are whole, six are
divided breadthwise, each in two squares,
and three by a lengthwise cut, each in t\vo
columns ; altogether making thirty-six pieces.
The children soon become acquainted with
this Gift, as the variety of forms is much less
than in the preceding one, where, by an ob-
lique division of the cubes, an entirely new
radical principle was introduced.
It is here, therefore, mainly the proportions
of size of the oblongs, squares, and columns
contained in this Gift and the number of each
kind of these bodies, about which the child
has to become enlightened, before engaging
in building — playing, creating — withthis new
material.
The cube is placed upon the table — all parts
are disjoined — then equal parts collected
2S
GUIDE TO KINDER-GARTNERS.
into groups, and the child is then asked,
"How many blocks have you altogether?"
How many oblongs? how many squares?
how many columns ? Compare the sides of
the blocks with another — take an oblong —
how many squares do you need to cover it ?
how many columns ?
Place the oblong upon its long edge, now
upon its shortest side — and state how many
squares or columns you need in order to
reach its height, in either case. Exercises of
this kind will instruct the child sufficiently,
to allow it to proceed, in a short time, to the
individual creating, or producing occupation
with this new Gift.
FORMS OF LIFE.
(PLATES XVri. AND XVIH.)
It is the forms of life, particularly, for
which this Gift provides material, far better
fitted, than any previously used. The ob-
longs admit of a much larger extension of
the plane, and allow the enclosure of a much
more extensive hollow space, than was possi-
ble, for instance, with the cubes of the Fifth
Gift. Innumerable forms can therefore be
produced with this Gift, and the attention and
interest of the pupil will be constantly in-
creased.
This very variety, however, should induce
the careful teacher to prevent the child's
purely accidental production of forms. It is
always necessary to act according to certain
rules and laws, to reach a certain aim. The
established principle, that one form should al-
ways be derived from another, can be carried
out here only with great difficulty, owing to
the peculiarity of the material. It is therefore
frequently necessary, particularly with the
more complicated structures, to lay an entirely
new foundation for the building to be erected.
It is necessary, at all times, to follow the
child in his operations, — his questions should
always be answered and suggestions made to
enlarge the circle of ideas.
It affords an abundance of pleasure to a
child to observe that we understand it and
its work ; it is, therefore, a great mistake in
education to neglect to enter fully into the
spirit of the pupil's sphere of thinking and
acting; and if we ever should allow our-
selves to go so far as to ridicule his pro-
ductions, instead of assisting him to improve
on them, we would certainly commit a most
fatal error.
The selections of forms of life on Plates
XVII. and XVIII., nearly all of which are
in the meantime forms of art and knowledge,
because of their architectural fundamental
forms, and the mathematical proportions of
their single parts, can, therefore, not fail to
give nourishment to various powers of the
mind.
1. House without roof; back wall has no
door, i", ground plan.
2. Colonnade ; lowest row, five oblongs
laid lengthwise, and back wall consisting of
ten standing oblongs, upon which ten squares.
2', ground plan.
3. Hall, with columns.
4. Summer House. 4% ground plan ; ves-
tibule formed by six columns.
5. Memorial Column of the Three Friends.
5°, ground plan.
6. Monument in Honor of "Some Fallen
Hero. 6°, ground plan; lowest row, eight
oblongs ; second square of nine squares, par-
tially constructed of oblongs ; third, four sin-
gle squares ; then four columns, four single
squares, square of nine squares, square of
four squares, etc.
7. Facade of a Large House. 7°, ground
plan.
8. The Columns of the Three Heroes.
8% ground plan.
9. Entrance to Hall of Fame. 9°, ground
plan ; first row, sLx squares and six oblongs ;
second row, six oblongs ; third row, six
squares, etc.
10. Two Story House, with yard. io%
ground plan. Io^ side view.
11. Faqade. II^ ground plan.
12. Covered Summer House. 12°, ground
plan.
GUIDE TO KINDER-GARTNERS.
29
13. Front View of a Factory. 13°, ground
plan. I3^ side view.
14. Double Colonnade. 14°, ground plan.
15. An Altar. 15°, ground plan.
16. Monument. 16°, ground j^lan.
17. Columns of Concord. 17", ground
plan.
The fantasy of the child is inexhaustibly
rich in inventing new forms. It creates gar-
dens, yards, stables with horses and cattle,
household furniture of all kinds, beds with
sleeping brothers and sisters in them, tables,
chairs, sofas, etc., etc.
If several children combine their individual
building they produce large structures, perfect
barn-yards with all out-buildings in them, nay,
whole villages and towns. The ideas that in
union there is strength, and that by co-oper-
ation great things may be accomplished, will
thus early become manifest to the young
mind.
FORMS OF BEAUTY.
(plates XIX. AND XX.)
The forms of beauty of this Gift offer far less
diversity than those of Gift No. 5 ; owing, how-
ever, to the peculiar proportions of the plane,
they present sufficient opportunity for charac-
teristic representations, not to be neglected.
We give on the accompanying plates a sin-
gle succession of development of such forms.
The progressive changes are easily recog-
nized, as the oblong, which needs to be moved
to produce the following figure, is always
marked by a letter. The center-piece always
consists of two of the little columns, standing
one upon another, and important modifica-
tions may be produced by using the oblongs
in lying or standing positions. By employing
the four little columns in various ways, many
pleasant changes can be produced by them.
FORMS OF KNOWLEDGE.
(plate XX.)
These also appear in much smaller num-
bers compared with the richness and multi-
plicity of the Fifth Gift. By the absence of
oblique (obtuse and acute) angles, they are
limited to the square and oblong, and exer-
cises introduced with these previously, may
be repeated here with advantage.
All Froebel's Gifts are remarkable for the
peculiar feature that they can be rendered ex-
ceedingly instructive by frequently introduc-
ing repetitions under varied conditions and
forms, by which means we are sure to avoid
that dry and fatiguing monotony which must
needs result from repeating the same thing in
the same manner and form. And still more,
the child, thereby, becomes accustomed to
recognize like in unlike, similarity in dissimi-
larity, oneness in multiplicit}', and connection
in the apparently disconnected.
In Fig. 16-22, all squares that can be
formed with the Sixth Gift are represented.
In Fig. 23 we see a transition from the forms
of knowledge to those of beauty.
With the Sixth Gift we reach the end of
the two series of development given by
Froebel in the building blocks, whose aim
is to acquaint the child with the general
qualities of the solid body by own observa-
tion and occupation with the same.
THE SEVENTH GIFT.
SQUARE AND TRIANGULAR TABLETS FOR LAYING OF FIGURES.
(plates XXI. TO XXIX.)
All mental development begins with con-
crete beings. The material world with its
multiplicity of manifestations first attracts
the senses and excites them to activitj', thus
causing the rudimental operations of the
mental powers. Gradually — only after many
processes, little defined and explained by any
science as yet, have taken place — man be-
comes enabled to proceed to higher mental
activity, from the original impressions made
upon his senses by the various surroundings
in the material world.
The earliest impressions, it is true, if often
repeated, leave behind them a lasting trace
on the m.ind. But between this attained pos-
sibility to recall once-made observations, to
represent the object perceived by our senses,
by mental image (imagination), and the
real thinking or reasoning, the real pure ab-
straction, there is a very long step, and
nothing in our whole system of education is
more worthy of consideration than the sud-
den and abrupt transition from a life in the
concrete, to a life of more or less abstract
thinking to which our children are submitted
when entering school from the parental
house.
Froebel, by a long series of occupation *
material, has successfully bridged over this
chasm, which the child has to traverse, and
the first place among it, the laying tablets of
various forms occupy.
The series of tablets is contained in five
boxes containing—
A. Quadrangular square tablets.
B. Right angular (equal sides). ^ „ .
C. Right angular (unequal sides). I .
D. Equilateral, and {Tu^t
E. Obtuse angular (equal sides). J
The child was heretofore engaged with
solid bodies, and in the representation of
real things. It produced a house, garden,
sofa, etc. It is true the sofa was not a sofa
as it is seen in reality ; the one built by the
child was, therefore, so to say, an image al-
ready, but it was a bodily image, so much so
that the child could place upon it 'a little
something representing its doll. The child
considered it a real sofa, and so it was to the
child, fulfilling, as it did, in its little world,
the purposes of a real sofa in real life.
With the tablets, the embodied planes, the
child can not represent a sofa, but a form
similar to it ; an image of the sofa can be pro-
duced by arranging the squares and triangles
in a certain order.
We shall see, at some future time, how
Froebel continues on this road, progressing
from the plane to the line, from the line to
the point, and finally enables the child to
draw the image of the object, with pencil or
pen in his own little hand.
A. THE QUADRANGULAR LAYING TAB-
LETS (Squares).
(PLATE XXI.)
They are given the child first to the num-
ber of six. In a similar way as was done
with the various building gifts, the child is
led to an acquaintance with the various quali-
GUIDE TO KINDER GARTNERS.
ties of Ihe new material, and to compare it,
with other things, possessing similar qualities.
It is advisable to let the child understand
the connection existing between this and the
previous gifts. The laying tablets are nothing
but the embodied planes, or separated sides
of the cube. Cover all the sides of a cube
with square tablets and after the child has
recognized the cube in the body thus formed,
let it separate the tablets one by one, from
the cube hidden by them.
The following, or similar questions are here
to be introduced : — What is the form of this
tablet ? How many sides has it ? How
many angles ? Look carefully at the sides.
Are they alike or unlike each other? They
are all alike. Now look at the corners. These
also are all alike. Where have you seen sim-
ilar figures ?
What are such figures called ? Can you
show me angles somewhere else ? Where
the two walls meet is an angle. Here, there,
and everywhere you find angles.
But all angles are not alike, and they are
therefore differently named. All these dif-
ferent names you will learn successively, but
now let us turn to our tablet. Place it right
straight before you upon the table. Can you
tell me now what direction these two sides
have which form the angle ? The one is
horizontal, the other perpendicular. An
angle which is formed if a perpendicular
meets a horizontal line, is called a right an-
gle. How many of such angles can you
count on your tablet? Four. Show me such
right angles somewhere else.
By the acquisition of this knowledge the
child has made an important step forward.
Looking for horizontal and perpendicular
lines, and for right angles, it is led to investi-
gate more deeply the relations of form, which
it had heretofore observed only in regard to
the size conditioned by it.
The child's attention should be drawn to
the fact that, however the tablet may be
placed the angles always remain right angles
though the lines are horizontal and perpen-
dicular only in four positions of the tablet,
namely, those where the edges of the tablet
are placed in the same direction with the
lines on the table before the child. This
will give occasion to lead the child to a gen-
eral perception of the standing or hanging of
objects according to the plummet.
But the tablet will force still another ob-
servation upon the child. The opposite sides
have an equal direction ; they are the same
distance from each other in all their points ;
they never meet, however many tablets the
child may add to each other to form the lines.
The child learns that such lines are called
parallel lines. It has observed such lines
frequently before this, but begins just now to
understand their real being and meaning.
It looks now with much more interest than
ever before at surrounding tables, chairs,
closets, houses, with their straight line orna-
ments, for now the little cosmopolitan does
not only receive the impressions made by the
surroundings upon his senses, but he already
looks for something in them, an idea of which
lives in his mind. Although unconscious of
the fact that with the right angle and the
parallel line, h€< received the elements of
architecture, it will pleasantly incite him to
new observations whenever he finds them
again in another object which attracts his
attention.
The teacher in remembrance of oar oft-
repeated hints, will proceed slowly, and care-
fully, according to the desire and need of the
child. She repeats, explains, leads the child
to make the same observations in the most
different objects, and changing circumstances,
or guides the child in laying other forms of
knowledge (lying or standing parallelograms
Fig. 4 and 5) of life, (steps. Fig. 6 and 8,
double steps. Fig. 7 and 9, door, Fig. 10, sofa.
Fig. II, cross. Fig. 12), or forms of beauty.
The number of these forms is on the whole
only very limited. It is well now to augment
the number of tablets in the hands of the
pupil, by two, when a much larger munber of
forms can be produced. The various series
32
GUIDE TO KINDER GARTNERS.
of forms of beauty, introduced with the third
Gift, can be repeated here and enlarged upon,
according to the change in tlie material now
at the disposal of the child.
B, RIGHT-ANGLED TRIANGLES.
(PLATE XXI.)
As from the whole cube, the divided cube
was produced, so by division the triangle
springs from the square. By dividing it
diagonally in halves, we produce the rectan-
gular triangle with equal sides.
Although the form of the triangle was pre-
sented to the child in connection with the
Fifth Gift, it here appears more independentl)-,
and it is not only on that account necessary
to acquaint the child with the qualities and
being of the new addition to its occupation
material, but still more so as the forms of
the triangles with which, as a natural sequence
it will have to do hereafter, were entirely
unknown to the pupil. The child places two
triangles, joined to a square, upon the table.
What kind of a line divides your four-cor-
nered tablet.' An oblique or slanting line.
In what direction does the line cut your
square in two ? From the right upper corner
to the left lower corner. Such a line we call
a diagonal.
Separate the two parts of the square, and
look at each one separately. What do you
call each of these parts ? What did you call
the whole ? A square. How many corners
or angles had the square ? Four. How many
corners or angles has the half of the square
you are looking at? Three. This half,
therefore, is called a triangle, because, as I
have explained to you before, it has three
angles. How many sides has your tri-
angle ? etc.
Looking at the sides more attentively,
what do you observe ? One side is long, the
other two are shorter, and, like each other.
These latter are as large as the sides of the
square, all sides of which were alike.
Now tell me what kind of angle it is, that
is formed by these two equal sides ? It is a
right angle. Why? and what will you call
the other two angles ? How do the sides
run which form these two angles ? They run
in such a way as to form a very sharp point,
and these angles are, therefore, called acute
angles, which means sharp-pointed angles.
Your triangle has then, how many different
kinds of angles ? Two ; one right angle, and
two acute angles.
It is not necessary to mention that the
above is not to be taught in one lesson. It
should be presented in various conversations,
lest the acquired knowledge might not be
retained by even the brightest child. The
attention of the pupil may also be led, in
subsequent con\^ersations to the fact that the
largest side is opposite the largest angle, and
that the two acute angles are alike, etc.
Sufficient opportunity for these and additional
remarks will offer itself during the represen-
tations of forms of life, of knowledge, and of
beauty, for which the child will employ its
tablets, according to its own free will, and
which are not necessarily to be separated,
neither here nor in any other part of these
occupations, although it is well to observe a
certain order at any time.
Whenever it can be done, elementary knowl-
edge may well be imparted, together with the
representations of forms of life, and forms of
beauty.
In order to invent, the child must have
observed the various positions which a trian-
gle may occupy. It will find these acting
according to the laws of opposites, already
familiar to the child.
The right angle, to the right below, (Fig. 17)
it will bring into the opposite direction to the
left above, (Fig. 18) then into the mediative
positions to the left below, (Fig. 19) and to
the right above, (Fig. 20). By turning, it
comes aboi'e\h& long side, (Hypothenuse, Fig.
21) then opposite below it, (Fig. 22) then to
the right, (Fig. 23) and finally to the left of
it, (Fig. 24).
The various positions of two triangles are
easily found by moving one of them around
GUIDE TO KINDER-GARTNERS.
33
the other. Fig. 26-31 are produced from
Fig. 25, by moving the triangle marked a,
always keeping it in its original position,
around the otlier triangle.
In Figs. 32-37, the changes are produced,
alternating regularly between a turn and a
move of the triangle a. In Figs. 38-47,
simply turning takes place.
After the child has become acquainted with
the first elements from which its formations
develop, it receives for a beginning four of
the triangled tablets. It then places the
right angles together, and thereby forms a
standing full square, (Fig. 48.)
By placing the tablets in an opposite posi-
tion', turning the right angles from within to
without, it produces a lying square with the
hollow in the middle, (Fig. 49). This hollow
space has the same shape and dimensions as
Fig. 48. The child will fancy Fig. 48 into the
place of this hollow space, and will thereby
transfer the idea of a full square upon an
empty or hollow one, and will consequently
make the first step from the perception of the
concrete to its idea, the abstraction.
The child will now easily find mediative
forms between these two opposites. It places
two right angles v.'ithin and two without,
(Fig. 58 and 59) two above, and two below,
(Fig. 50) two to the right, and two to the left,
(Fig. 50-
So far, two tablets always remained con-
nected with one another. By separating
them we produce the new mediative forms,
52, 53, 54 and 55. in which again two and
two are opposites. But instead of the right.
the acute angles may meet in a point also,
and thus Figs. 56 and 57 are produced,
which are called rotation forms, because the
isolated position of the right angle suggests,
as it were, an inclination to fall, or turn, or
rotate.
The mediation between these two oppo-
site figures is given in Figs. 50 and 5 1 —
between them and Figs. 49 and 50 in Figs.
58 and 59 ; and it should be remarked in
this connection, that these opposites are con-
5
ditioned by the position of the right angle in
all these cases.
All these exercises accustom the pupil to a
methodic handling of all his material. They
develop a correct use of his eye, because
regular figures will only be produced when
his tablets are placed correctly and exactly
in their places shown by the net-work on the
table. The precaution which must be exer-
cised by the child not to disturb the easily
movable tablets, and the care employed to
keep each in its place, are of the greatest
importance for future necessary dexterity of
hand. In a still greater degree than by these
simple elementary forms just described, this
will be the case, when the pupil comes into
possession of the following boxes, containing
a larger number — up to sixty-four — tablets for
the formation of more complicated figures,
according to the free exercise of his fantasy.
FORMS OF LIFE.
(plate xxiii.)
All hints given in connection with the build-
ing blocks, are also to be followed here, with
this difference only, that we produce now .
images of objects, whereas, heretofore, we
united the objects themselves.
The child here begins —
A, WITH FOUR TABLETS.
And forms witli them —
I. A flower-pot. 2. A little garden-house.
3. A pigeon-house.
B, WITH EIGHT TABLETS.
4. A cottage. 5. A canoe or boat. 6.
A covered goblet. 7. A lighthouse. 8. A
clock.
C, WITH SI.XTEEN TABLETS.
9. A bridge with two spans. 10. A large
gate. II. A church. 12. A gate with bel-
fry. 13. A fruit basket.
D, WITH THIRTY-TWO TABLETS.
14. A peasant's house. 15. A forge with
high chimney. 16. .'\ coffee-mill. 17. A cof-
fee-pot without handle.
34
GUIDE TO KINDER-GARTNERS.
E, WITH SIXTY-FOUR TABLETS.
i8. A two-Story house. 19. Entrance to a
railroad depot. 20. A steamboat.
In No. 21, we see the result of combined
activity of many children. Although to some
grown persons it may appear as if the images
produced do not bear much resemblance to
what they are intended to represent, it should
be remembered that iu most cases, the chil-
dren themselves have given the names to
the representations. Instructive conversation
should also prevent this drmvmg with planes,
as it were, from being a mere mechanical pas-
time ; the entertaining, living word must in-
fuse soul into the activity of the hand and its
creations. Each representation, then, will
speak to the child and each object in the
world of nature and art will have a story to
tell to the child in a language for which it
will be well prepared.
We need not indicate how these conversa-
tions should be carried on, or what they
should contain. Who would not think, in
connection with the pigeon-house, of the
beautiful white birds themselves, and the nest
they build ; the white eggs they lay, the ten-
der young pigeons coming from them, and
the care with which the old ones treat the
young ones, until they are able to take care
of themselves. An application of these re-
lations to those between parents and children,
and, perhaps, those between God and man,
who, as his children enjoy his kindness and
love every moment of their lives, may be
made, according to circumstances — all de-
pending on the development of the children.
However, care should always be taken not to
present to them, what might be called ab-
stract morals, which the young mind is unable
to grasp, and which, if thus forced upon it
cannot fail to be injurious to moral develop-
ment. The aim of all education should be
love of the good, beautiful, noble, and sub-
lime ; but nothing is more apt to kill this
very love, ere it is born, than the monotony
of dry, dull preaching of morals to young
children. Words not so much as deeds —
actual experiences in tiie life of the child, are
its most natural teachers in this important
branch of education.
FORMS OF BEAUTY.
(PLATES XXI. AND XXII.)
Owing to the larger multiplicity of ele-
mentary forms to be made with the triangles,
the number of Forms of Beauty is a very large
one. Triangle, square, right angle, rhomb,
hexagon, octagon, are all employed, and the
great diversity and beauty of the forms pro-
duced lend a lasting charm to the child's
occupation. Its inventive power and desire,
led by law, will find constant satisfaction, and
to give satisfaction in the fullest measure
should be a prominent feature of all systems
of education.
FORMS TO BE BUILT WITH FOUR TABLETS
have already been mentioned on page 33, as
contained on Plate XXI — D, 48-59. We find
more satisfaction by employing
EIGHT TABLETS.
In working with them, we can follow the
most various principles. Series E, 60-69, is
formed by doubling the forms produced by
four tablets ; series F, starting from the fun-
damental form 70, making one half of the
tablets move from left to right, the length of
one side, with each move. A new series
would be produced, if we move from right to
left in a similar manner. In these figures,
sides always touch sides, and corners touch
corners — consequendy, parts of the same kind.
The transition or mediation between these
two opposites, the touching of corners and
sides, would be produced by shortening the
movement of the traveling triangle one-half,
permitting it to proceed one-half side only.
But let us return to fundamental form 70.
In it, either large sides (hypothenuses) or
small sides (catheti) constantly touch one
another. The opposite — large side touching
small — we have in Fig. 82, and by traveling
from right to left of half the triangles, series
GUIDE TO KINDER-GARTNERS.
35
G, 82 to 87, is produced. We would have
produced a much larger number of forms, if
we had not interrupted progress by turning
the triangles produced by Fig. 86.
In the fundamental forms 70 and 82, the
sides touched one another. Fig. 88 shows
that they may touch at the corners only. In
this figure, the right angles are without ; in
89 and 90, they are within. Fig. 90 is the
mediation between 70 and 89, for four tablets
touch with their sides (70) four with the cor-
ners (89). No. 91 is the opposite of 90, full
center, (empty center.) and mediation between
88 and 89 — (four right angles without, as in
88, and four within, as in 89.) It is already
seen, from these indications, what a treasure
of forms enfolds itself here, and how, with
SIXTEEN TABLETS,
it again will be multiplied.
It would be impossible to exhaust them.
Least of all, should it be the task of this
work to do this, when it is only intended to
show how the productive selfoccupation of
the pupil can fittingly be assisted. We be-
lieve, besides, that we have given a .suffi-
cient number of ways on which fantasy may
travel, perfectly sure of finding constantly
new, beautiful, eye and taste developing for-
mations. We, therefore, simply add the series
J and K, the first of which is produced by
quadrupling some of the elementary forms
given at D, 48 to 59, and the second of which
indicates how new series of forms of beauty
may be developed from each of these forms.
It must be evident, even to the casual ob-
ser\-er, how here also the law of opposites,
and their junction, was obsen^ed. Opposites
are 92 and 93 ; mediation, 94 and 95 :' oppo-
sites, 96 and 97 ; mediation, 98, 99, and 100:
opposites, loi and 102 ; mediation, 103, etc.
WITH THIRTY-TWO TABLETS.
As heretofore, we proceed here also in the
same manner, by multiplying the given ele-
ments, or by means of further development,
according to the law of opposites. As an
example, we give Series L, the members of
which are produced by a four-fold junction
of the elements 68 and 69. no and iii are
opposites; 112 and 113 mediative forms.
WITH SIXTV-FOUR TABLETS.
Here, also, the combined activity of many
children will result in forms interesting to be
looked at, not only by little children. There
is another feature of this combined activity
not to be forgotten. The children are busy
obeying the same law ; the same aim unites
them — one helps the other. Thus the condi-
tions of human society — family, community,
states, etc., — are already here shown in their
effects. A system of education which, so to
speak, by mere play, leads the child to appre-
ciate those requisites, by compliance with
which it can successfully occupy its position
as man in the future, certainly deserves the
epithet of a natural and rational one.
Figures 114, 115, 116, are enlarged pro-
ductions from 96 and 97. They are planned
in such a way, as to admit of being continued
in all directions, and thus serve to carry out
the representation of a veiy large design.
After having acted so far, according to in-
dications made here, it is now advisable to
start from the fundamental forms presented
in the Fifth Gift, and to use them, with the
necessary modifications, in forther occupying
the pupils with the tablets. Fig. 117 gives
a model, showing how the motives of the
Fifth Gift can be used for this purpose.
FORMS OF KNOWLEDGE.
(plate XXII.)
By joining two, four, and eight tablets, we
have already become acquainted with the
regular figures which may be formed with
them, namely, triangle, quadrangle (square),
right angle, rhomboid, and trapezium (Plate
XXII., Figs. 1 18-123).
The tablets are, however, especially quali-
fied to bring to the observation of the child
different sizes in equal forms (similar figures),
and equal sizes in different forms.
36
GUIDE TO KINDER- GARTNERS.
Figures 124, 125, and 126 show triangles
of wliich each is the half of the following,
and Nos. 129, 127, and 128, three squares
of that kind. Figures 1 19-123, and 129-
131, show the former five, the latter three
times the same size in different forms.
That the contemplation of these figures,
the occupation with them, mu'st tend to facili-
tate the understanding of geometrical axioms
in future, who can doubt? And who can
gainsay that mathematical instruction, by
means of Froebel's method, must needs be
facilitated, and better results obtained ? That
such instruction, then, will be rendered more
fruitful for practical life, is a fact which will
be obvious to all, who simply glance at our
figures, even without a thorough explanation.
They contain demonstratively the larger num-
ber of the axioms in elementary geometry,
which relate to the conditions of the plane in
regular figures.
For the present purpose, it is sufficient if
the child learns to distinguish the various kinds
of angles, if it knows that the right angles
are all equally large, the acute angles smaller,
and the obtuse angles larger than a right
angle, which the child will easily understand
by putting one upon another. A deeper in-
sight in the matter must be reserved for the
primary department of instruction.
C. THE EQUILATERAL TRIANGLE.
(plates XXIV. AND X.XV.)
So far the right angle has predominated in
the occupations with the tablets, and the
acute angle only appeared in subordinate
relations. Now it is the latter alone which
governs the actions of the child in producing
forms and figures.
The child will compare the equilateral
triangle, which it receives in gifts of 3, 6, 9,
and 12, first with the isosceles, right-angled
tablet already known to him. Both have three
sides, both three angles, but on close observa-
tion not only their similarities, but also their
dissimilarities will become apparent. The
three angles of the new triangle are all smaller
than a right angle, are acute angles and the
three sides are just alike,- hence the name —
equilateral — meaning "■ eqtcal sided" triangle.
Joining two of these equilateral tablets the
child will discover that it cannot form any
of the regular figures previously produced.
No triangle, no square, no right angle, no
rhomboid, can be produced, but only a form
similar to the latter, a rhomboid with four
equal sides. To undertake to produce forms
of life with these tablets would prove very
unsatisfactory. Of particular interest, how-
ever, because presenting entirely new forma-
tions, are
THE FORMS OF BEAUTY.
The child first receives three tablets and
will find the various positions of the same
towards one another according to the law of
opposites and their combination. Vide Plate
XXIV., 1-9.
SIX TABLETS.
The child will unite his tablets around one
common center (Fig. 10), form the opposite
(Fig 11), and then arrive at the forms of me-
diation 12, 13, 14, and 15, or it unites three
elementary forms each composed of two tab-
lets as done in 16, and forms the opposite
17 and the mediations 18 and 19, or it starts
from No. 10, turning first i, then 2, then 3
tablets, outwardly. By turning one tablet,
21 and 22, by turning two tablets, 23, 24, 25,
26, 27, 28 and 29, are produced from No. 20.
This may be continued with 3, 4, and 5 tab-
lets. All forms thus received give us ele-
mentary forms which may be employed as
soon as a larger number of tablets are to be
used. ^
NINE TABLETS.
As with the right-angled triangle, small
groups of tablets were combined to form
larger figures, so we also do here. The ele-
mentary forms under A give us in threefold
combination the series of forms under C, 30 —
40, which in course of the occupation may be
multiplied at will.
GUIDE TO KINDER-GARTNERS.
37
TWELVK TABLETS.
(PLATE XXV.)
Half of the tablets are painted brown, the
balance l)lue By this difterence in color, op-
positis are rendered more conspicuous, and
these twelve tablets thus aftbrd a splendid
opportunity for illustrating more forcibly the
law of opposites and their combination.
Plate XXV. shows how, by combination of
opposites in the forms a and b, every time
the star c is produced. Entirely new series of
forms may be produced by employing a larger
number of tablets, i8, 24 or 36. We are,
however, obliged to leave these representa-
tions to the combined inventive powers of
• teacher and pupil.
FORMS OK RXOWl.EDGE.
It has been mentioned before, that the
previously introduced regular mathematical
tlgures do not appear here as a whole. How-
ever, a triangle can be represented by four or
nine tablets, a rhomboid by four, six or eight
tablets, a trapezium l)y three, and manifold
instructive remarks can be made and experi-
ences gathered in the construction of these
figures. But above all, it is the rhombus
and hexagon, with which the pupil is to be
made acquainted here. The child unites two
triangles by joining side to side, and thus
produces a rhombus.
The child compares the sides — are they
alike ? What is their direction ? Are they
parallel ? Two and two have the same di-
rection, and are therefore parallel.
The child now examines the angles and
finds that two and two are of equal size.
'I'hey are not right angles. Triangles, smaller
than right angles, he knows, are called acute
angles, and he hears now that the larger
ones are called olMuse angles. The teacher
may remark that the latter are twice the size
of the former ones. By these remarks the
pupil will gradually receive a correct idea of
the rlionibus and of the qualities by which it
is distinguished from the quadrangle, right
angle, trapezium and rhomboid.
6
In the same manner, the hexagon gives
occasion for interesting and instructive ques-
tions and answers. How many sides has it ?
How many are parallel ? How many angles
does it contain ? What kind of angles are
the)- ? How large are they as compared with
the angles of the equal sided triangle.' Twice
as large.
The power of observation and the reason-
ing faculties are constantly developed by such
conversation, and the results of such exer-
cises are of more importance than all the
knowledge that may be acquired in the mean-
time.
The greater part of this occupation, how-
ever, is not within the Kinder-Garten proper,
but belongs to the realm of the Primary'
School Department. If thej' are introduced
in the former, they are intended only to swell
the sum of general experience in regard to
the qualities of things, whereas in the latter,
they serve as a foundation for real knowledge
in the department of mathematics.
D. THE OBTUSE-ANGLED TRIANGLE WITH
TWO SIDE.S ALIKE.
(plates xxvl and xxvil)
The child receives a box with sixty-four
obtuse-angled tablets. It examines one of
them and compares it with the right-angled
triangle, with two sides alike. It has two
sides alike, has also two acute angles, but the
third angle is larger than the right angle ; it
is an obtuse angle, and the tablet is, there-
fore, an obtuse-angled triangle with two sides
alike.
The pupil then unites two and two tablets
by joining their sides, corners, sides and
corners, and vice versa, as shown in Figs. 1-8,
on Plate XXVI.
The next preliminary exercise, is the com-
bination, by fours, of elementary forms thus
produced. Peculiarly beautiful, mosaic-like
forms of beauty result from this process.
The Pigs. 9-15 aftbrd examples which were
produced by combination of two opposites,
a and b, or by mediative forms c and d. In
38
GUIDE TO KINDER-GARTNERS.
Figs. 16-22 we have finally some few sam-
ples of forms of life.
The forms of knowledge which may be
produced, afford opportunity to repeat what
has been taught and learned previously about
proportion of form and size. In the Primary
School the geometrical proportions are further
introduced, by which irjeans the knowledge
of the pupils, in regard to angles, as to the
position they occupy in the triangle, can be
successfully developed by practical observa-
tion, without the necessity of ever dealing in
mere abstractions.
E. THE RIGHT-ANGLED TRIANGLE WITH
NO EQUAL SIDES.
(PLATES XXVIII. AND XXIX.)
The little box with fifty-six tablets of the
above description, each of which is half the
size of the obtuse-angled triangle, enables the
child to represent a goodly number of forms
of life, as shown on Plate XXIX.
In producing them, sufficient opportunities
will present themselves, to let the child find out
the qualities of the new occupation material.
A comparison with the right angled triangle
with two equal sides will facilitate the matter
greatly.
On the whole, howe^■er, the process of de-
velopment may be pursued, as repeatedly in-
dicated on previous occasions.
The variety of the forms of beaut)' to be laid
with these tablets, is especially founded on
their combination in twos. Plate XXVIII.,
Figs. 1-6, shows the forms produced by join-
ing equal sides.
In similar manner, the child has to find out
the forms which will be the result of joining
unlike sides, like corners, unlike corners, and
finally, corners and sides.
By a fourfold combination of such element-
ary forms the child receives the material,
(Figs. 7-18,) to produce a large number of
forms of beauty similar to those given under
19-22.
For the purpose, also, of presenting to the
child's observation, in a new shape, propor-
tions of form and size, in the production of
forms of knowledge, these tablets are very
serviceable.
Like the previous tablets, these also, and a
following set of similar tablets, are used in
the Primary Department for enlivening the
instruction in Geometry. It is believed that
nothing has ever been invented to so facilitate,
and render interesting to teacher and pupil,
the instruction in this so important branch of
education as the tablets forming the Seventh
Gift of Froebel's Occupation Material, the use
of which is commenced with the children when
they have entered the second year of their
Kinder-Garten discipline.
THE EIGHTH GIFT.
STAFFS FOR LAYING OF FIGURES.
(PLATES XXX. TO XXXIII.)
As the tablets of the Seventh Gift are
nothing but an embodiment of the planes sur-
rounding or limiting the cube, and as these
planes, limits of the cube, are nothing but
the representations of the extension in length,
breadth, and height, already contained in the
sphere and ball, so also the staffs are derived
from the cube, forming as they do, and here
bodily representing its edges. But they are
also contained in the tablets, because the
plane is thought of, as consisting of a con-
tinued or repeated line, and this may be
illustrated by placing a sufficient number of
one inch long staffs side by side, and close
together, until a square is formed
The staffs lead us another step farther,
from the material, bodily, toward the realm
of abstractions.
By means of the tablets, we were enabled
to produce flat images of bodies ; the slats,
which, as previously mentioned, form a tran-
sition from plane to line, gave, it is true, the
outlines of forms, but these outlines still re-
tained a certain degree of the plane about
them ; in the staffs, however, we obtain the
material to draw the outlines of objects, by
bodily lines, as perfectly as it can possibly
be done.
The laying of staffs is a favorite occupa-
tion with all children. Their fantasy sees in
them the most different objects, — stick, yard
measure, candle ; in short, they are to them
representatives of every thing straight.
Our staffs are of the thickness of a line
(one twelfth of an inch), and are cut in vari-
7
ous lengths. The child, holding the staff in
hand, is asked : What do you hold in your
hand.? How do you hold it? Perpendicu-
larly. Can you hold it in any other way.'
Yes ! I can hold it horizontally. Still in
another way? Slanting from left above, to
right below, or from right above to left
below.
Lay your staff upon the table. How does
it lie ? In what other direction can you place
it? (Plate XXX. A.)
The child receives a second staff. How
many staffs have you now ? Now try to form
something. The child lays a standing cross,
(Fig. 4.) You certainly can lay many other
and more beautiful things ; but let us see
what else we may produce of this cross, by
moving the horizontal staff, by half its lengfth,
(Fig. B. 4 to 14.) Starting from a lying cross,
(C. 15 — 23) or from a pair of open tongs,
(where two acute and two obtuse angles are
formed by the crossing staffs,) and proceeding
similarly as w-ith B, we will produce all posi-
tions which two staffs can occupy, relative to
one another, except the parallel, and this will
give ample opportunit}- to refresh, and more
deeply impress upon the pupil's mind, all that
has been introduced so far, concerning per-
pendicular, horizontal, and oblique lines, and
of right, acute and obtuse angles. With two
staffs, we can also form little figures, which
show some slight resemblance with things
around us. By them we enliven the power of
recollection and imagination of the child, ex-
ercise his abilit}' of comparison, increase his
40
GUIDE TO KINDER-GARTNERS.
treasure of ideas, and develop, in all these
his power of perception and conception — the
most indispensable requisites for disciplining
the mind.
Our plates give representations of the fol-
lowing objects :
WITH TWO STAFFS.
Fig. 24. A Playing Table.
Fig. 25. A Weather-vane.
Fig. 26. A Pickax.
Fig. 27. An Angle measure. (Carpenter's
square.)
Fig. 28. A Candle stick.
Fig. 29. Two Candles.
Fig. 30. Rails.
Fig. 31. Roof
WITH THREE STAFFS.
Fig. 32 A Kitchen Table.
Fig. 33. A Garden Rake.
Fig. 34
A Flail.
WITH SEVEN STAFFS.
Fig. 35-
An Umbrella.
Fig. 74. A Window.
Fig. 36.
A Hay Fork.
Fig. 75. A Stretcher.
Fig. 37-
A Small Flag.
Fig. 76. A Dwelling-house.
Fig. 38.
A Steamer.
Fig. 77. Steeple with Lightning-rod.
Fig. 39-
A Whorl.
Fig. 78. A Balance.
Fig. 40.
A Star.
Fig. 79. Piano-forte.
Fig. 80. A Bridge with Three Spans
WITH FOUR STAFFS.
Fig. 81. An Inn Sign.
Fig. 41-
A Small Looking-glass.
Fig. 82. Crucifix and Two Candles.
Fig. 42.
A Wooden Chair.
Fig. 83. Tombstone and Cross.
Fig. 43-
A Wash-bench.
Fig. 84. Rail Fence.
Fig. 44-
Kitchen Table with Candle.
Fig. 85. Garret Window.
Fig. 45-
A Crib.
Fig. 86. Flower Spade.
Fig. 46.
A Kennel.
Fig. 87. A Star Flower.
Fig. 47-
Sugar-loaf.
Fig. 48.
Flower pot.
WITH EIGHT STAFFS.
Fig. 49-
. Signal-post.
Fig. 88. Book-shelves.
Fig. 5°-
Flower-stand.
Fig. 89. Church, with Steeple.
Fig. 51-
Crucifix.
Fig. 90. Tombstone and Cross.
Fig 52-
A Grate.
Fig. 91. Gas Lantern.
Fig. 92. Windmill.
WITH FIVE STAFFS.
Fig. 93. A Tower.
Fig. S3-
Signal Flag of R. R. Guard.
Fig. 94. An Umbrella.
Fig. 54.
Chest of Drawers.
Fig. 95. A Carrot.
Fig- 55-
A Cottage.
Fig. 96. A Flower-pot.
Fig. 56
A Steeple.
Fig. 57-
A Funnel.
Fig. 58.
A Beer Bottle.
Fig. 59.
A Bath Tub.
Fig. 60.
A (broken) Plate.
Fig. 61.
A Roof
Fig. 62.
A Hat.
Fig. 63.
A Chair.
Fig. 64.
A Lamp Shade.
Fig. 65.
A Wine-glass.
Fig. 66.
A Grate.
WITH SIX STAFFS.
Fig. 67. A Large Frame.
Fig. 68. A Flag.
Fig. 69. A Barn.
Fig. 70. A Boat.
Fig. 71. A Reel.
Fig. 72. A Small Tree.
Fig 73. A Round Table.
GUIDE TO KINDER-GARTNERS.
Fig. 97. A large Wash tub.
Fig. 98. A large Rail Fence.
Fig. 99. A large Kitchen Table.
Fig 100. A Shoe.
Fig. 1 01. A Butterfly.
Fig. 102. A Kite.
WITH NINE STAFFS.
Fig. 103. Church with Two Steeples.
Fig. 104. Dwelling-house.
Fig. 105. Coffee-mill.
Fig. 106. Kitchen Lamp.
Fig. io7. Sail-boat.
Fig. loS. Balance.
WITH TEN STAFFS.
Fig.
109. A Tower.
Fig.
no. A Drum.
Fig.
III. Grave-yard Wall.
Fig.
112. A Hall.
Fig.
113. A Flowerpot.
Fig.
114. A Street Lamp.
Fig.
115. A Satchel.
Fig.
116. A Double Frame.
Fig.
117. A Bedstead.
Fig.
118. A row of Barns.
Fig.
119. A Flag.
WITH ELEVEN STAFFS.
Fig.
1 20. A Kitchen Lamp.
Fig.
121. A Pigeon-house.
Fig.
122. A Farm-house.
Fig.
123. A Sail-boat.
Fig.
124. A Student's Lamp.
WITH TWELVE STAFFS.
Fig.
125. A Church.
Fig.
126. A Window.
Fig.
127. Chair and Table.
Fig.
128. A Well with Sweep.
These exercises are to be continued with a
larger number of staffs. The hints given
above, will enable the teacher to conduct the
laying of staffs in a manner interesting, as well
as useful, for her pupils.
It is advisable to guide the activity of the
child occasionally in another direction. The
pupils may all be called upon to lay tables,
which can be produced from two to ten staffs, or
houses which can be laid with eighteen staffs.
Another change in this occupation can be
introduced by employing two, four, or eight
times, divided staffs. It is obvious that, in
this manner, the figures may often assume a
greater similarity and better proportions than
is possible if only staffs of the same length are
employed.
If a staff is not entirely broken through,
but only bent with a break on one side, an
angle is produced. If a staff forms several
such angles, it can be used to represent a
curved or rounded line, and by so doing a new
feature is introduced to the class.
Staffs are also employed for representing
forms of beauty. The previous, or simulta-
neous occupation with the building blocks,
and tablets, will assist the child in producing
the same in great variety. Figures 121 — 124
on Plate XXXIII. belong to this class of repre-
'sentations.
Combination of the occupation material of
several, or all children taking part in the ex-
ercises, will lead to the production of larger
forms of life, or beauty, which in the Primary
Department, can even be extended to repre-
senting whole landscapes, in which the mate-
rial is augmented by the introduction of saw-
dust to represent foliage, grass, land, moss,
etc. Plate XXXIII. gives, un(3er Fig. 120, a
specimen of such a production-^-on a very re-
duced scale.
By means of combination, the children
often produce forms which afford them great
pleasure, and repay them for the careful per-
severance and skill employed. .They often
express the wish that they might be able to
show the production to father, or mother, or
sister, or friend. But this they cannot do, as
the staffs will separate when taken up.
We should assist the little ones in carrying
out their desire, of giving pleasure to others,
by showing to, or presenting them with the
result of their own industry, in portable form.
42
GUIDE TO KINDER-GARTNERS.
By wetting the ends of the staffs with mucil-
age, or binding them together with needle
and thread, or placing them on substantial
paper, we can grant their desire, and make
them happy, and be sure of their thanks for
our efforts.
We employ the same means of rendering
permanent the production of staff-laying in
our instruction in reading, where letters are
fastened to paper by mucilage, thus impress-
ing upon the child's mind more lastingly, the
visible signs of the sounds he has learned.
But we have still another means of render-
ing these representations permanent, and it is
by drawing, which, on its own account, is to
be practiced in the most elementary manner.
We begin the drawing, as will hereafter be
shown, as a special branch of occupation, as
soon as the child has reached its third or
fourth year.
The child is provided with a slate, upon
whose surface, a net-work of horizontal and
perpendicular lines is drawn. Instead of lay-
ing the staff upon the table, the child places
it upon the slate. Taking the staff from its
place, he draws with the slate pencil, in its
stead, a line as long as the staff, in the same
direction. He draws the perpendicular staff.
The horizontal, slantingly laid staff, is drawn
in all its variations in like manner, perpendic-
ular, and horizontal ; perpendicular and ob-
lique, or horizontal and oblique staffs are
brought in contact with one another, and
these connections reproduced by drawing.
The method of laying staffs is in general
the same, applied for drawing, the latter, how-
ever, progresses less rapidly. It is advisable
to combine staffs in regular figures, triangles
and squares, and to find out in a small num-
ber of such figures all possible combinations
according to the law of opposites. Plates
XXIV. and XXV. will furnish material for this
purpose.
All these occupations depend on the larger
or smaller number of staffs employed ; they
therefore afford means for increasing and
strengthening the knowledge of the child.
The pupil, however, is much more decidedly
introduced into the elements of ciphering,
when the staffs are placed into his hands for
this specific purpose. We do not hesitate to
make the assertion that there is no material
better fitted to teach the rudiments in figures,
as also the more advanced steps in arithme-
tic, than Froebel's staffs, and that by their in-
troduction, all other material is rendered use-
less. A few packages of the staffs in the
hands of the pupil is all that is needed in the
Kinder Garten proper, and the following De-
partment of the Primary.
The children receive a package with ten
staffs each. Take one staff and lay it per-
pendicularly on the table. Lay another at
the side of it. How many staffs are now be-
fore you ? Twice one makes two.
Lay still another staff upon the table.
How many are there now? One and one
and one — two and one are three.
Still another, etc., etc., until all ten staffs
are placed in a similar manner upon the
table. Now take away one staff. How many
remain ? Ten less one leaves nine. Take
away another staff from these nine. How
many are left.' Nine less one leaves eight
Take another; this leaves ? seven, etc.,
etc., until all the staffs are taken one by one
from the table, and are in the child's hand
again. Take two staffs and lay them upon
the table, and place two others at some dis-
tance from them. (|| ||) How many are now
on the table ? Two and two are four. Lay
two more staffs beside these four staffs. How
many are there now ? Four and two are six.
Two more. How many are there now ? Six
and two are eight. And still another two.
How many now ? Eight and two are ten.
The child has learned to add staffs by twos.
If we do the opposite, he will also learn to
subtract by twos. In similar manner we pro-
ceed with three, four, and_;?z.'^. After that, we
alternate, with addition and subtraction For
instance, we lay three times two staffs upon the
table and take away twice two, adding again
four times two. Finally we give up the
GUIDE TO KINDER- GARTNERS.
43
equality of the number and alternate, by ad-
ding different numbers. We lay upon the
table 2 and 3 staffs=5, adding 2=7 adding
3=10. This affords opportunity to intro-
duce 6 and 9, as a whole, more frequently
than was the case in previous exercises. In
subtraction we observe the same method, and
introduce exercises in which subtraction and
addition alternate with unequal numbers.
Lay 6 staffs upon the table, take 2 away, add
4, take away i, add 3, and ask the child how
many staffs are on the table, after each of
these operations.
In like manner, as the child learned the
figures from one to ten, and added and sub-
tracted with them as far as the number of 10
staffs admitted, it will now learn to use the
lo's up to 100. Packages of 10 staffs are
distributed. It treats each package as it did
before the single staff. One is laid upon the
table, and the child says, "Once ten ;" add a
second, " Twice ten ; " a third, " Three times
ten," etc. Subsequently it is told, that it is
not customary to say twice, or two times ten,
but twenty; not three times ten, but thirty,
etc. This experience will take root so much
the sooner, in his memory, and become
knowledge, as all this is the result of his own
activity.
As soon as the child has acquired sufficient
ability in adding and subtracting by tens, the
combination of units and tens is introduced.
The pupil receives two packages of ten
staffs — places one of them upon the table,
opens the second and adds its staffs one by
one to the ten contained in the whole pack-
age. He learns 10 and i = ii, 10 and 2=12,
10 and 3 = 13, until 10 and 10 = 20 staffs.
Gathering the 10 loose staffs, the child re-
ceives another package and places it beside
the first whole package. 10 and 10=20
staffs. Then he adds one of the loose staffs,
and says 20 and 1=21,20 and 2 = 22, etc.
Another package of 10 brings the number to
31, etc., etc., up to 91 staffs. In this manner
he learns 22, 32, up to 92, 23 to 93, and 100,
and to add and subtract within this limit.
To be taught addition and subtraction in
this manner, is to acquire sound knowledge,
founded on self-activity and experience, and
is far superior to any kind of mind-killing
memorizing usually employed in this connec-
tion.
If addition and subtraction are each other's
opposites, so addition and multiplication on
the one hand, and subtraction and division
on the other, are oppositionally equal, or,
rather, multiplication and division are short-
ened addition and subtraction.
In addition, when using equal numbers of
staffs, the child finds that by adding 2 and 2
and 2 and 2 staffs it receives 8 staffs, and is
told that this may also be expressed by saying
4 times 2 staffs are 8 staffs. It will be easy
to see how to proceed with division, after the
hints given above.
It has been previously mentioned that for
the representation of forms of life and beauty,
the staffs frequently need to be broken. This
provides material for teaching fractions, in the
meantime. The child learns by observtion
i staff, i, -J, i, etc. The proportion of the
part or of several equal parts to the whole,
becomes clear to him, and finally it learns to
add and subtract equal fractions, in element-
ary form, in the same rational manner.
Let none of our readers misunderstand us
as intimating that all this should be accom-
plished in the Kinder-Garten proper.
Enough has been accomplished if the child
in the Kinder Garten, by means of staffs and
other material of occupation, has been en-
abled to have a clear understanding of figures
in general.
This will be the basis for further develop-
ment in addition, subtraction, multiplication
and division in the Primaiy Department.
It now remains to add the necessary advice
in regard to the introduction and representa-
tion with staffs of the nuvierah. In order to
make the children understand what nnmerals
are, use the blackboard and show them that
if we wish to mark down how many staffs,
blocks, or other things each of the children
44 ■
GUIDE TO KINDER-GARTNERS.
have, we might make one Hne for each staff,
block, etc. Write then one small perpendicu-
lar line on the blackboard, saying in writing,
Charles has one staff; making hiw lines below
the first, continue by saying, Emma has two
blocks; again, making three lines, Ernest has
three rubber balls, and so on until you have
written ten lines, always giving the name of
the child and stating how many objects it has.
Then write opposite each row of lines to the
right, the Arabic figure expressing the number
of lines, and remark that instead of using so
many lines, we can also use these figures,
which we call numerals. Then represent with
the little staff these Arabic figures, some of
which require the bending of some of the
staffs, on account of the curved lines.
After the children have learned that the
figures which we use for marking down the
number of things are called numerals, exer-
cises of the following character may be intro-
duced :
How many hands has each of you .' Two.
The numeral 2 is written on the board. How
many fingers on each hand ? Five. This is
written also on the board — 5. How many
walls has this room ? Four. Write this figure
also on the board. How many days in the
week are the children in the Kinder-Garten ?
Six days. The 6 is also written on the board.
Then repeat, and let the children repeat
after you, as an exercise in speaking, and at
the same time, for the purpose of recollecting
the numerals :
Each child has 2 hands, on each hand are
5 fingers ; this room has 4 walls, — always
emphasizing the numerals, and pointing to
them when they are named.
The children may then count the objects in
the room, or elsewhere, and then lay, with
their staffs, the numerals expressing the num-
ber they have found, speaking in tlie mean-
time, a sentence asserting the fact which they
have stated.
After having introduced the numerals in
this manner, the teacher, on some following
day, may proceed to reading exercises.
The second part of this Guide contains
systematically arranged material for instruc-
tion in reading, according to the phonetic
method.
Suffice it to say, tliat it is begun in the
same manner in which numerals were intro-
duced. As by means of numerals, I could
mark on the blackboard the number of things,
so I can also mark on the board the names of
things, their qualities and actions. In doing
this I write words, and zcords consist of let
ters. Besides the words expressing names of
things, their qualities and actions, which are
the most important words in every language,
there are other words which are used for
other purposes. Such words are, for example,
no, now, never. Should I ask you, is any one
of you asleep, what would you answer ? " No,
sir. We are all awake." I will write the lit-
tle word " no," on the blackboard, because it
is the most important word in your answer.
There it stands, " no." And now I will ask you :
"Have you ever been in a Kinder-Garten?"
" Yes, sir, we are now in a Kinder-Garten
school." I will write on the board the little
wox^," now." There it stands, " w^w ;" and
another question I will now ask you : " Should
we ever kill an animal for the mere pleasure
of hurting it ? " " No, sir, «67rr." I will also
write the word " nex'er" on the board. There
it is, '■'■never." I will now pronounce these
three words for you, and each of you will
repeat them in the same manner in which I
do. N o! N ow! N ever! Chil-
dren, in repeating, always dwell on the n
sound longer than on any other part of the
word. They are then led to observe the
similarity of sound in pronouncing the three
words, then to observe the similarity of the
first letter in all of them, and finally the dis-
similarity of the remaining part of the words
in sound, and its representations — the letters.
I will now take away these words from
the blackboard, and write something else upon
it. I again write the " n" and the children
will soon recognize it as the letter previously
shown.
GUIDE TO KINDER-GARTNERS.
45
For the continuation of instruction in read-
ing, we refer tlie reader to the second part of
the " Guide," where all necessary information
on this important branch of instruction will
be found.
As the occupation with laying staffs, is one
of the earliest in the Kinder Garten, and is em-
ployed in teaching numerals, and reading and
writing, and drawing also, it is evident how
important a material of occupation was sup-
plied by Froebel, in introducing the staffs as
one of his Kinder-Garten Gifts.
THE NINTH GIFT.
WHOLE AND HALF RINGS FOR LAYING FIGURES.
Immediately connected with the staffs, or
straight lines, Froebel gives the representa-
tives of the rounded, curved lines, in a box
containing twenty-four whole and fort}'-eight
half circles of two different sizes made of
wire. We have heretofore introduced the
curved line by bending the staff; this, how-
ever, was a rather imperfect representation.
The rings now introduced supply the means
of representing a curved line perfectly, be-
sides enabling us by their different sizes to
show " the one within another " more plainly
than it could be done with the staffs, as the
above, upon, below, aside of each other, etc., could
well be represented, but not the " within " in
a perfectly clear manner.
This Gift is introduced in the same way as
all other previous Gifts were introduced, and
the rules by which this occupation is carried
on must be clear to every one who has fol-
lowed us in our " Guide " to this point.
The child receives one whole ring and two
half rings of the larger size. Looking at the
whole ring the children obser\'e that there is
neither beginning nor end in the ring — that it
represents the circle, in which there is neither
beginning nor end. With the half ring, they
have two ends ; half rings, like half circles
and all other parts of the circle or curved
lines, have two ends. Two of the half rings
form one whole ring or circle, and the chil-
dren are asked to show this by experiment,
(Fig. I, Plate XXXIV). Various observations
can be made by the children, accompanied by
remarks on the part of the teacher. When-
ever the child combined two cubes, two tablets,
staffs or slats with one another, in all cases
where corners and angles and ends were con-
cerned in this combination, corners and angles
were again produced. The two half rings or
half circles, however, do not form any angles.
Neither could closed space be produced by
two bodies, planes, nor lines ! — the two half
circles, however, close tightly up to each
other, so that no opening remains.
The child now places the two half circles
in opposite directions, (Fig. 2.) Before the
ends touched one another, now the middle of
the half circles ; previously a closed space
was formed, now both half circles are open,
and where they touch one another, angles
appear.
Mediation is formed in Fig. 3, where both
half circles touch each other at one end and
remain open, or, as indicated by the dotted
line, join at end and middle, thereby enclosing
a small plane and forming angles in the mean-
time.
Two more half circles are presented. The
child forms Fig. 4, and develops by moving
46
GUIDE TO KINDER-GARTNERS.
the half circles in the direction from without,
to within Fig 5, 6, 7, and 8.
The number of circles is increased. Fig.
9, 10, and II show some forms built of 8 half
circles.
All these forms are, owing to the nature of
the circular line, forms of beauty, or beauti-
ful forms of life, and, therefore, the occupa-
tion with these rings, is of such importance.
The child produces forms of beauty with
other material, it is true, but the curved line
suggests to him in a higher degree than any-
thing else, ideas of the beautiful, and the
simplest combinations of a small number of
half and whole circles, also bear in themselves
the stamps of beauty.
If the fact cannot be refuted, that merely
looking at the beautiful, favorably impresses
the mind of the grown person, in regard to
direction of its development, enabling him to
more fully appreciate the good, and true, and
noble, and sublime, this influence, upon the
tender and pliable soul of the child, must
needs be greater, and more lasting. Without
believing in the doctrine of two inimical
natures in man, said to be in constant con-
flict with each other, we do believe that the
talents and disposition in human nature are
subject to the possibility of being developed
in two opposite directions. It is this possi-
bility, which conditions the necessity of edu-
cation, the necessity of employing every
means to give the dormant inclinations and
tastes in the child, a direction toward the
true, and good, and beautiful, — in one word,
toward the ideal. Among these means, stands
pre-eminently a rational and timely develop-
ment of the sense of beauty, upon which
Froebel lays so much stress.
Showing the young child objects of art which
are far beyond the sphere of its appreciation
however, will assist this development, much
less than to carefully guard that its surround
ings contain, and show the fundamental req
uisites of beauty, viz. : order, cleanliness, sim
plicity, and harmony of form, and giving as^
sistance to the child in the active representa
tion to the beautiful in a manner adapted to
the state of development in the child himself.
Like forms laid with staffs, those repre
sented with rings and half rings also, are
imitated by the children by drawing them on
slate or paper.
THE TENTH GIFT.
THE MATERIAL FOR DRAWING.
(PLATES XXXV. TO
•) -
One of the earliest occupations of the child
should be methodical drawing. Froebel's
opinion and conviction on this subject, de-
viates from those of other educators, as much
as in other respects. Froebel, however, does
not advocate drawing, as it is usually prac-
ticed, which on the whole, is nothing else but
a more or less thoughtless mechanical copy-
ing. The method advanced by Froebel, is in-
vented by him, and perfected in accordance
with his general educational principles.
The pedagogical effect of the customary
method of instruction in drawing, rests in
many cases simply in the amount of trouble
caused the pupil in surmounting technical
difficulties. Just for that reason it should be
GUIDE TO KIXDER-GARTNERS.
47
abandoned entirely for the youngest pupils,
for the difficukics in many cases are too great
for the child to cope with. It is a work of
Sisyphus, labor without result, naturally tend-
ing to extirpate the pleasure of the child in its
occupation, and the unavoidable consequence
is that the majority of people will never reach
the point where they can enjoy the fruits of
their endeavors.
If we acknowledge that Froebel's educa-
tional principles are correct, namely, that all
manifestations of the child's life are manifes-
tations of an innate instinctive desire for
development, and therefore should be fos.
tered and developed by a rational education,
in accordance with the laws of nature. Draw-
ing should be commenced with the third year;
nay, its preparatory principles should be intro-
duced at a still earlier period.
With all the gifts, hitherto introduced, the
children were able to study and represent
forms and figures. Thus they have been
occupied, as it were, in drawing with bodies.
This developed their fantasy, and taste, giving
them in the meantime correct ideas of the
solid, plane, and the embodied line.
A desire soon awakes in the child, to rep-
resent by drawing these lines and planes,
these forms and objects. He is desirous of
representation when he requests the mother
to tell him a story, explain a picture. He is
occupied in representation when breathing
against the window-pane, and scrawling on it
with its finger, or when trying to make figures
in the sand with a little stick. Each child is
delighted to show what it can make, and
should be assisted in every way to regulate
this desire.
Drawing not only develops the power of
representing things the mind has perceived,
but affords the best means for testing how far
they have been perceived correctly.
It was Froebel's task to invent a method
adapted to the tender age of the child, and
its slight dexterity of hand, and in the mean-
time to satisfy the claim of all his occupa-
tions, i. €., that the child should not simply
imitate, but proceed, self-actingly, to perform
work which enables him to reflect, reason,
and finally to invent himself.
Both claims have been most ingeniously
satisfied by Froebel. He gives the three
years' old child a slate, one side of w^hich is
covered by a net-work of engraved lines (one-
fourth of an inch apart), and he gives him in
addition, thereto, the law of opposites and
their mediation as a rule for h's activity.
The lines of the net-work guide the child in
moving the pencil, they assist it in measuring
and comparing situation and position, size
and relative center, and sides of objects.
This facilitates the work greatly, and in con-
sequence of this important assistance the
childs' desire for work is materially increased ;
whereas, obstacles in the earliest attempts at
all kinds of work must necessarily discourage
the beginner.
Drawing on the slate, with slate pencil is
followed by drawing on paper with lead
pencil. The paper of the drawing books is
ruled like the slates. It is advisable to begin
and continue the exercises in drawing on
paper, in like manner as those on the slate
were begun and continued, with this differ-
ence only, that owing to the progress made
and skill obtained by the child, less repeti-
tions may be needed to bring the pupil to
perfection here, as was necessary in the use
of the slate.
It has been repeatedly suggested, that
whenever a new material for occupation is
introduced, the teacher should comment upon,
or enter into conversation with the children,
about the same ; the difference between draw-
ing on the slate and on paper, and the mate-
rial used for both may give rise to many
remarks and instructive conversation.
It may be mentioned that the slate is first
used, because the children can easily correct
mistakes by wiping out what they have made,
and that they should be much more careful in
drawing on paper, as their productions can
not appear perfectly clean and neat if it
should be necessary to use the rublier often.
48
GUIDE TO KINDER- GARTNERS.
Slate and slate pencil are of the same mate-
rial ; paper and lead pencil are two very differ-
ent things. On the slate the lines and figures
drawn, appear white on darker ground. On
the paper, lines and figures appear black on
white ground.
More advanced pupils use colored lead
pencils instead of the common black lead
pencils. This adds greatly to the appear-
ance of the figures, and also enables the child
to combine colors tastefully and fittingly. For
the development of their sense of color, and
of taste, these colored mosaic like figures are
excellent practice.
Drawing, as such, requires observation, at-
tention, conception of the whole and its parts,
the recollection of all, power of invention and
combination of thought. Thus, by it, mind
and fantasy are enriched with clear ideas and
true and beautiful pictures. For a free and
active development of the senses, especially
eye and feeling, drawing can be made of in-
calculable benefit to the child, when its natu-
ral instinct for it is correctly guided at its
very awakening.
Our Plates XXXV. to XLVI. show the sys-
tematic course pursued in the drawing depart-
ment of the Kinder-Garten. The child is first
occupied by
THE PERPENDICULAR LINE.
(PLATES XXXV. TO XXXVIII.)
The teacher draws on the slate a perpen-
dicular line of a single length (^ of an inch),
saying while so doing, I draw a line of a single
length downward. She then (leaving the line
on the slate, or wiping it out) requires the
child to do the same. She should show that
the line she made commenced exactly at the
crossing point of two lines of the net-work,
and also ended at such a point.
Care should be exercised that the child
hold the pencil properly, not press too much
or too little on the slate, that the lines drawn
be as equally heavy as possible, and that each
single line be produced by one single stroke
of the pencil. The teacher should occasion-
ally ask : What are you doing ? or, what have
you done? and the child should always an-
swer in a complete sentence, showing that it
works understandingly. Soon the lines may
be drawn upwards also, and then they may
be made alternately up and down over the
entire slate, until the child has acquired a cer-
tain degree of ability in handling the pencil.
The child is then required to draw a per-
pendicular line of two lengths, and advances
slowly to lines of three, four and five lengths,
(Plate XXXV., Figs. 2—5).
With the number five Froebel stops on
this step. One to five are sufficiently known,
even to the child three years old, by the
number of his fingers.
The productions thus far accompHshed are
now combined. The child draws, side by
side of one another, lines of one and two
lengths (Fig. 6), of one, two and three lengths
(Fig. 7), of one, two, three and four lengths
(Fig. 8), and finally lines of one, two, three,
four and five lengths (Fig. 9.) It always forms
by so doing a right-angled triangle. We
have noticed already, in using the tablets, that
right-angled triangles can lie in many different
ways. The triangle (Fig. 9 and 10) can also
assume various positions. In Fig. 10 the
five lines stand on the baseline — the smallest
is the first, the largest the last, the right an-
gle is to the right below. In Fig. 1 1 the op-
posite is found — the five lines hang on the
base-line, the largest comes first, the smallest
last, and the right angle is to the left above.
Figs. 12 and 13 are forms of mediation of 10
and II.
The child should be induced to find Figs.
IT to 13 himself Leading him to understand
the points of Fig. 10 exactly, he will have no
difficulty in representing the opposite. Instead
of drawing the smallest line first, he will draw
the longest ; instead of drawing it downward,
he will move his pencil upward, or at least
begin to draw on the line which is bounded
above, and thus reach 11. By continued re-
flection, entirely within the limits of his capa-
bilities, he will succeed in producing 12 and 13.
GUIDE TO KINDER-GARTNERS.
49
Thus, by a different way of combination of
five perpendicular lines, four forms have been
produced, consisting of equal parts, being,
however, unlike, and therefore oppositionally
alike.
Each of these figures is a whole in itself.
But as every thing is always part of a larger
whole, so also these figures serve as elements
for more extensive formations.
In this feature of Froebel's drawing method,
in which we progress from the simple to the
more complicated in the most natural and
logical manner, unite parts to a whole and
recognize the former as members of the latter,
discover the like in opposites, and the media-
tion of the latter, unquestionable guarantee
is given that the delight of the child will be
renewed and increased, throughout the whole
course of instruction. Let Figs. lo — 13 be
so united that the right angles connect in
the center (Fig. 14), and again unite them so
that all right angles are on the outside (Fig.
15.) Figs. 14 and 15 are opposites. No. 14
is a square with filled inside and standing on
one corner; No. 15 one resting on its base,
with hollow middle. In 14 the right angles
are just in the middle; in 15 they are the
most outward corners. In the forms of medi-
ation (16 and 17), they are, it is true, on the
middle line, but in the meantime on the out-
lines of the figures formed. In the other
forms of mediation, (Figs. 18, 19, etc) they
lie altogether on the middle line ; but two in
the middle, and two in the limits of the
figure.
Thus we have again, in Figs. 18 — 22, four
forms consisting of exactly the same parts,
which therefore are equal and still have qual-
ities of opposites. In the meantime, they
are fit to be used as simple elements of fol-
lowing formations. In Fig. 22, they are com-
bined into a star with filled middle ; in Fig.
23, it is shown how a star with hollow middle
may be formed of them. (The Fig. 23, on
Plate XXXVI., does not show the lower part;
on Plate XXII., Fig. 97, Gift Seventh, the
whole star is shown.) Here, too, numerous
forms of mediation may be produced, but we
will work at present with our simple elements.
Owing to the similarity in the method of
drawing to that employed in the laying of the
right angled, isosceles triangle, it is natural
that we should here also arrive at the so-called
rotation figures, by grouping our triangles with
their acute angles toward the middle (Figs.
24 and 25), or arrange them around a hollow
square (Figs. 26 and 27.)
Figs. 28 and 29 are forms of mediation
between 24 and 25, and at the same time
between 14 and 15.
All these forms again serve as material for
new inventions. As an example, we produce
Fig. 30, composed of Figs. 28 and 29.
The number of positions in which our orig-
inal elements (Figs. 10 — 13) can be placed
by one another, is herewith not exhausted by
far, as the initiated will observ^e. Simple and
easy as this method is rendered by natural
law^s, it is hardly necessary to refer to the tab-
lets (Plates XXI. to XXIX..) which will sug-
gest a sufficient number of new motives for
further combinations.
As previously remarked, the slate is ex-
changed for a drawing-book as soon as the pro-
gress of the child warrants this change. It
aflfords a peculiar charm to the pupil to see his
productions assume a certain durability and
permanency enabling him to measure, by thera,
the progress of growing strength and ability.
So far the triangles produced by co arrange-
ment of our five lines, were right-angled.
Other triangles, however, can be produced
also. This, however, requires more practice
and security in handling the pencil.
Figs. 31 and 32 show an arrangement of
the 5 lines, of acute angled (equilateral) tri-
angles; Figs. 31 and 32 being opposites.
Their union gives the opposites 33 and 34 ;
finally, the combination of these two. Fig. 35.
In the last three figures we also meet now
the obtuse angle. This finds its separate
representation in the manner introduced in
Fig. 36 ; opposition according to position is
given in Fig. 37 ; mediation in Figs. 38 and
50
GUIDE TO KINDER-GARTNERS.
39, and the combination of these four ele-
ments in one rhomboid in Fig. 40. The four
obtuse angles are turned inwardly. Fig. 42,
the opposite of 40, is produced by arranging
the triangles in such a manner that the obtuse
angles are turned outwardly. Fig. 41 pre-
sents the form of mediation. Another one
might be produced by arranging the 4 obtuse
angled triangles represented in Nos. 36, 37,
38, and 39 in such a manner as to have 39
left above, 37 right above, 36 left below, and
39 I 37
38 right below. Thus : ~r\—^
36 I 38
It is evident that with obtuse angled trian-
gles, as with right angled triangles, combina-
tions can be produced. Indeed, the pupil
who has grown into the systematic plan of
development and combination will soon be
enabled to unite given elements in manifold
ways ; he will produce stars with filled and
hollow middle, rotation forms, etc., and his
mental and physical power and capacity will
be developed and strengthened greatly by
such inventive exercise.
Side by side with invention of forms of
beauty and knowledge, the representation of
forms of life, take place, in free individual ac-
tivity. The child forms, of lines of one length,
a plate, (Fig. 43,) or a star, (Fig. 44,) of lines
of one and two lengths a cross, (Fig. 45,) of
lines up to 4 lengths, it represents a coffee-
mill, (Fig. 46,) and employs the whole material
of perpendicular lines at his command, in the
construction of a large building with part of a
wall connected with it. (Fig. 47.) Equal
consideration, however, is to be bestowed
upon the opposite of the perpendicular,
THE HORIZONTAL LINE.
(PLATE XXXIX.)
The child learns to draw lines of a single
length below each other, then lines of 2, 3, 4,
and 5 lengths, (Figs, i — 5.) It arranges them
also beside each other, (Figs. 6 — 8) unites
lines of i and 2 lengths, (Fig. 9,) of i, 2, and
3 lengths, (Fig. 10,) of i to 4 lengths, (Fig. 1 1,)
finally of i to 5 lengths, thereby producing
the right angled triangle 12, its opposite 13,
and forms of mediation 14 and 15. The
pupil arranges the elements into a square
with filled middle, (Fig. 16) with hollow mid-
dle, (Fig. 17) produces the forms of mediation,
cl a dib
(Fig. 18, — — and — — ) and continues to
b I d a j c
treat the horizontal line just as it has been
taught to do with the perpendicular. ( By turn-
ing the Plates XXXV. to XXXVIII., the
figures on them will serve as figures with hori-
zontal lines.) Rotation forms, larger figures,
acute and obtuse angled triangles can be
formed ; forms of beauty, knowledge and life
are also invented here, (Fig. 19, adjustable
lamp J Fig. 20, key; Fig. 21, pigeon-house;)
and after the child has accomplished all this, it
arrives finally, in a most natural way, at the
COMBINATION OF PERPENDICULAR AND
HORIZONTAL LINES.
(plates XL. TO XLIL)
First, lines of one single length are com-
bined ; we already have four forms different
as to position, (Fig. i.) Then follow the
combination of 2, 3, 4, 5 — fold lengths, (Figs.
2 — 5) with each of which 4 opposites as to
position are possible. As previously, lines of i
to 5 — fold lengths are united to triangles, so
now the angles are united and Fig. 6 is pro-
duced. Its opposite, 7 and the forms of medi-
ation, can be easily found. A union of "these
four elements appears in the square, Fig. 8;
opposite Fig. 9. In Fig. 8, the right angles are
turned toward the middle, and the middle is
full. In Fig. 9, the reverse is the case. Forms
of mediation easily found. We have in Figs.
a i c bid
8 and 9 the combinations — 1 — and — |----
Let the following
dib
be constructed :
alb die dl
dib
b|d d|b b |d d
b I c aid
b ' b c ' a I d '
GUIDE TO KINDER-GARTNERS.
If perpendicular and horizontal lines can
be united only to form right angles, we have
previously seen that perpendicular as well as
horizontal lines may be combined to obtuse
and acute angled triangles. The same is pos-
sible, if they are united. Fig. lo gives us an
e-xample. All perpendicular lines are so ar-
ranged as to form obtuse angled triangles. By
their combination with the horizontal lines,
the element lo" is produced, its opposite lo'',
and the forms of mediation io'= and lo'' whose
combination forms Fig. lo.
As in Fig. lo, the perpendicular lines form
an obtuse angled triangle, so the horizontal
lines, and finally both kinds of lines can at
the same time be arranged into obtuse angled
triangles.
Thus a series of new elements is produced,
whose systematic employment the teacher
should take care to facilitate. (The scheme
given in the above may be used for this
purpose.)
So far we have only formed angles of lines
equal in length ; but lines of unequal lengths
may be combined for this purpose. Exactly
in the same manner as lines of a single length
were treated, the child now combines the line
of a single length with that of two lengths,
then, in the same way, the line of two lengths
with that of four lengths, that of three with
that of six, that of four with that of eight, and
finally, the line of five lengths with that of ten.
■ The combination of these angles affords new
elements with which the pupil can continue
to form interesting figures in the already well-
known manner. Figs, ii and 12, on Plate
XL., are such fundamental forms ; the de
velopment of which to other figures will give
rise to many instructive remarks. These fig-
ures show us that for such formations the
horizontal as well as the perpendicular line
may have the double length. Fig. 11 shows
the horizontal lines combined in such a way
as if to form an acute-angled triangle. They,
however, form a right-angled triangle, only the
right angle is not, as heretofore, at the end
of the longest line, but where? An acute-
angled triangle would result, if the horizontal
lines were all two net-squares distant from
each other. Then, however, the perpendicular
lines viould form an obtuse-angled triangle.
Important progress is made, when we com-
bine horizontal and perpendicular lines in
such a way that by touching in two points
they form closed figures, squares and oblongs.
First, the child draws squares of one-
length's dimension, then of two-lengths, of
three, four and five lines. These are combined
then as perpendicular lines were combined
also I- with 2-, the i^, 2^ and 3^ etc. These
combinations can be carried out in a perpen-
dicular direction, when the squares will stand
over or under each other; or in horizontal,
when the squares will stand side by side ; or,
finally, these two opposites may be combined
with one another.
Fig. 13° shows as an example a combina-
tion of four squares in a horizontal direction ;
13'' is the opposite ; c and d are forms of me-
diation.
In Fig. 14*, squares of the first, second and
third sizes are combined, perpendicularly and
horizontally, forming a right angle to the
right below ; b is the opposite, (angle left
above ;) c and d are forms of mediation. The
same rule is followed here as with the right
angle formed by single lines. The simple
elements are combined with each other into a
square with full or hollow middle, etc. ; and
from the new elements thus produced larger
figures are again created, as the example Fig.
15, Plate XLL, illustrates. From the four
elements 14"''"', the figure 15* and its opposite
B are constructed, (analogous to the manner
employed with Fig. 28, Plate XXXVII.,) a two-
fold combination of which resulted in Fig. 15.
Squares of from one to five length lines of
course admit of being combined in similar
manner. Each essentially new element should
give rise to a number of exercises, conditioned
only by the individual ability of the child. It
must be left to the faithful teacher, by an
earnest observation and study of her pupils,
to find the right extent, here as everywhere in
52
GUIDE TO KINDER- GARTNERS.
their occupations. Indiscriminate skipping
is not allowed, neither to pupil nor teacher ;
each following production must, under all cir-
cumstances be derived from the preceding one.
As the square was the result of angles
formed of lines of equal length, so also with
the oblong. Here too the child begins with
the simplest. It forms oblongs, the base of
which is a single line, the height of which is a
line of double length. It reverses the case
then. Base line 2, height single length. Re-
taining the same proportions, it progresses to
larger oblongs, the height of which is double
the size of its base, and vice versa, until it
has reached the numbers 5 and 10.
It is but natural that these oblongs, stand-
ing or lying, should also be united in perpen-
dicular, and horizontal directions. Each form
thus produced again assumes four different
positions, and the four elements are again
united to new formations, according to the
rules previously explained. Fig. 16" shows an
arrangement of standing oblongs, in horizontal
directions. The opposite would contain the
right angle, at a to the right below — to the
left above ; 16° would be one form of media-
tion, a second one, (opposite of 16^) would
have its right angle to the right above.
Fig. 17 shows a combination of lying ob-
longs, in a perpendicular direction. Fig. iS,
shows oblongs in perpendicular and horizon-
tal directions. Fig. 19, a combination of stand-
ing and lying oblongs, the former being ar-
ranged perpendicularly, the latter, horizon-
tally.
In Fig. 20, we find standing oblongs so
combined that the form represents an acute
angled triangle ; a and b are the only possible
opposites in the same.
These few examples may suffice to indicate
the abundance of forms which may be con-
structed with such simple material as the
horizontal and perpendicular lines, from i to
5 lengths, (and double.)
It is the task of the educator to lead the
learner to detect the elements, logically, in
order to produce with them, new forms in
unlimited numbers, within the boundaries of
the laws laid down for this purpose.
But even without using these elements, the
child will be able, owing to continued practice,
to represent manifold forms of life and beauty,
partly by its own free invention, partly by
imitating the objects it has seen before. As
samples of the former, Plate XLIL, Fig. 27,
shows a cross. Fig. 29, a triumphal gate. Fig.
30, a wind-mill, of the latter, Fig. 21 — 24, and
28, show samples of borders ; Fig. 25 and 26,
show other simple embellishments. As the
perpendicular line conditioned its opposite,
the horizontal line, both again condition their
mediation.
THE OBLIQUE LINE.
(plates xliii. to xlv.)
Our remarks here can be brief as the ope-
rations are nothing but a repetition of those
in connection with the perpendicular line.
The child practices the drawing of lines
from I to 5 lengths, (Plate XLIII., i to 5,)
and combines these, receiving thereby 4 op-
positionally equal right angled triangles, (Fig.
6 — 9,) of which it produces a square, (Fig. 10,)
its opposite, (Fig. 11,) forms of mediation, and
finally large figures.
Then the lines are arranged into obtuse
angles, and the same process gone through
with them.
With these, as in Fig. 13, its opposite 16,
and its forms of mediation, 14 and 15, the
obtuse angles will be found at the perpendic-
ular middle line, or as in 17, at the horizontal
middle line. By a combination of 15 and 17,
we produce a star, 19. Finally we have also,
reached here the formation of the acute
angled triangle, (Fig. 18.) The oblique line
presents particular richness in forms, as it
may be a line of various degrees of inclina-
tion. It is an oblique of the first degree
whenever it appears as the diagonal of a
square, as in Figs, i — 19. When it appears
as the diagonal of an oblong, it is either an
oblique of the 2d, 3d, 4th, or 5lh degree, ac-
cording to the proportions of the base line.
GUIDE TO KINDER-GARTNERS.
53
and height of tlie oblong, i to 2, i to 3, i to
4, I to 5.
In Fig. 20°, obliques of the second degree
are united to a right-angled triangle. 20" is
the opposite, 20° and d form mediations.
In Fig. 21, the same lines are united in an
obtuse angled triangle. In Fig. 22, they finally
form an acute angle.
In all these cases, the obliques were diag-
onals of standing oblongs. They may just as
well be diagonals of lying oblongs. Fig. 23,
in which obliques from the first to the fifth
degree are united, will illustrate this. The
obliques are here arranged one above the
other. In Fig. 24, the members a and b show
a similar combination ; the obliques, however,
are arranged beside one another ; the mem-
bers, c and d, are formed of diagonals of stand-
ing oblongs.
Obliques of various grades can be united
with one point, when the elements in Fig. 25,
will be produced, which requires the other
elements, b, c, and d, to form this figure, the
opposite of which would have to be formed
bid
according to the formula, — — , beside which
c I a
c I a
the forms of mediation would appear as — —
b 1 d
dlb
(Fig. 26) and — — .
a 1 c
As in this case, lying figures are produced,
standing ones can be produced likewise.
Each two of the elements thus received may
be united, so that all obliques issue from one
point, as in Fig. 27, and in its opposite. Fig. 28.
An oppositional combination can also take
place, so that each two lines of the same
grade meet, (Fig. 29.) The combination of
obliques with obliques to angles, to squares
and oblongs now follow, analogous to the
method of combining oblongs, perpendicular
and horizontal lines. Finally the combination
of perpendicular and oblique, horizontal and
oblique lines to angles, rhombus and rhomboid
■is introduced.
With these, the child tries his skill in pro-
ducing forms of life : Fig. 40, gate of a for-
tress; 41, church with school-house and cem-
etery wall, and forms of beauty: Figs. 30 — 39.
The task of the Kinder -Garten and the
teacher has been accomplished, if the child
has learned to manage oblique lines of the
first and second degree skillfully. All given
instaiction which aimed at something beyond
this, was intended for the study of the teacher
and the Primary Department, which is still
more the case in regard to —
THE CURVED LINE.
(plate -\LVI.)
Simply to indicate the progress, and to give
Froebel's system of instruction in drawing
complete, we add the following, and Plate
XLVI. in illustration of it.
First, the child has to acquire the ability to
draw a curved line. The simplest curved line
is the circle, from which all others may be
derived.
However, it is difficult to draw a circle, and
the net on slate and paper do not afford suffi-
cient help and guide for so doing. But on
the other hand, the child has been enabled to
draw squares, straight and oblique lines, and
with the assistance of these it is not difficult
to find a number of points which lie on the
periphery of a circle of given size.
It is known that all corners of a quadrangle
(square or oblong) lie in the periphery of a
circle whose diameter is the diagonal of the
quadrangle. In the same manner all other
right angles constructed over the diameter,
are periphery angles, affording a point of the
desired circular line. It is therefore nec-
essary to construct such right angles, and this
can be done very readily with the assistance
of obliques of various grades.
Suppose we draw from point a (Fig. i) an
oblique of the third degree, as the diagonal
of a standing oblong ; draw then, starting
from point c, an oblique of the third degree, as
diagonal of a lying oblong, and continue both
these lines. They will meet in point a, and
there form a right angle.
54
GUIDE TO KINDER-GARTNERS.
All obliques of the same degree, drawn
from opposite points, will do the same as
soon as the one approaches the perpendicular
in the same proportion in which the other
comes near the horizontal, or as soon as the
one is the diagonal of a standing, the other
of a lying oblong.
The lines Aa and Cc are obliques of the
third, Ab and Cb of the second, Af and C/
of the third degree, etc., etc. In this manner
it is easy to find a number of points, all of
which are points in the circular line, intended
to be drawn. Two or three of them over
each side, will suffice to facilitate the drawing
of the ciRCUMscribing circle, (Fig. 2.) In like
manner, the iNXERscribing circle will be ob-
tained by drawing the middle transversals of
the square, (Fig. 3,) and constructing from
their end-points angles in the previously de-
scribed manner.
After the pupil has obtained a correct idea
of the size and form of the circle, whose ra-
dius may be of from one to five lengths, it
will divide the same in half and quarter cir-
cles, producing thereby the elements for its
farther activity.
The course of instruction is here again the
same as that in connection with the perpen-
dicular line. The pupil begins with quarter
circles, radius of which is of a single length.
Then follow quarter circles with a radius of
from two to five lengths. By arrangement of
these five quarter circles, four elements are
produced, which are treated in the same man-
ner as the triangles produced by arrangement
of five straight lines. The segments may be
parallel, and the arrangement may take place
in perpendicular and horizontal direction, (Fig.
4 and 5,) or they may, like the obliques of va-
rious degrees, meet in one point, as in Fig. 8,
of which Figs. 4 and 5 are examples.
Fig. 6 represents the combination of the
elements a and (/ as a new element ; Fig. 7,
the combination of d and c. In Fig. 8 the
arrangement finally takes place in oblique
direction, and all lines meet in one point.
The quarter circle is followed by the half
circle 9, 10, 11 ; then the three-fourths circle
(Fig. 12), and the whole circle, as shown in
Fig. 13-
With the introduction of each new line, the
same manner of proceeding is observed.
Notwithstanding the brevity with which we
have treated the subject, we nevertheless
believe we have presented the course of in-
struction in drawing sufficiently clearly and
forcibly, and hope that by it we have made
evident :
1. That the method described here is per-
fectly adapted to the child's abilities, and fit
to develop them in the most logical manner ;
2. That the abundance of mathematical
perceptions offered with it, and the constant
necessity for combining according to certain
laws, can not fail to surely exert a wholesome
influence in the mental development of the
pupil ;
3. That the child thus prepared for future
instruction in drawing, will derive from such
instruction more benefit than a child prepared
by any other method.
Whosoever acknowledges the importance
of drawing for the future life of the pupil —
may he be led therein by its significance for
industrial purposes, or resthetic enjoyment,
which latter it may afford even the poorest ! —
will be unanimous with us in advocating an
early commencement of this branch of in-
struction with the child.
If there be any skeptics on this point, let
them try the experiment, and we are sure they
will be won over to our side of the question.
THE ELEVENTH AND TWELFTH GIFTS.
MATERIAL FOR PERFORATING AND EMBROIDERING.
(PLATES .\LVII. TO L.)
It is claimed by us that all occupation ma-
terial presented by Froebel, in the Gifts of the
Kinder-Garten, are, in some respects, related
to each other, complementing one another.
What logical connection is there between the
occupation of perforating and embroidering,
introduced with the present and the use of
the previously introduced Gifts of the Kinder-
Garten ? This question may be asked by
some superficial enquirer. Him we answer
thus : In the first Gifts of the Kinder-Garten,
the solid mass of bodies prevailed ; in the fol-
lowing ones the plane ; then the embodied line
was followed by the drawn line, and the occu-
pation here introduced brings us down to the
point. With the introduction of the per-
forating paper and pricking needle, we have
descended to the smallest part of the whole —
the extreme limit of mathc?natical divisibility ;
and in a playing manner, the child followed
us unwittingly, on this, in an abstract sense,
difficult journey.
The material for these occupations is a
piece of net paper, which is placed upon
some layers of soft blotting paper. The
pricking or perforating tool is a rather strong
sewing needle, fastened in a holder so as to
project about one-fourth of an inch. Aim of
the occupation is the production of the beau-
tiful, not only by the child's own activity, but
by its own invention. Steadiness of the eye
and hand are the visible results of the occu-
pation which directly prepares the pupil for
various kinds of manual labor. The per-
forating, accompanied by the use of the
needle and silk, or worsted, in the way em-
broidery is done, it is evident in vi'hat direc-
tion the faculty of the pupil may be developed.
The method pursued with this occupation
is analogous to that employed in the drawing
department. Starting from the single point,
the child is gradually led through all the
various grades of difficulty ; and from step to
step its interest in the work will increase,
especially as the various colors of the em-
broidered figures add much to their liveliness,
as do the colored pencils in the drawing
department.
The child first pricks perpendicular lines
of two and three lengths, then of four and five
lengths, (Figs. 2 and 3.) They are united to
a triangle, opposites and forms of mediation
are found, and these again are united into
squares with hollow and filled middle, (Figs.
4 and 5.) The horizontal line follows, (Figs.
6 — 8,) then the combination of perpendicu-
lar and horizontal to a right angle in its four
oppositionally equal positions, (Figs. 9 — 12.)
The combination of the four elements present
a vast number of small figures. If the exter-
nal point of the angle of 9 and 10 touch one
another, the cross (Fig. 13) is produced; if
the end points of the legs of these figures
touch, the square is made, (Fig. 14.) By
repeatedly uniting 9 and 12 Fig. 15 is pro-
duced, and by the combination of all four
angles Figs. 16 and 17. According to the
rules followed in laying figures with tab-
lets of Gift Seven, and in drawing, or by a
simple application of the law of opposites, the
56
GUIDE TO KINDER-GARTNERS.
child will produce a large number of other
figures.
The combination of lines of i and 2 lengths
is then introduced, and standing and lying
oblongs are formed, (Figs. 18 and ig,) etc.
The school of perforating, per se, has to con-
sider still simple squares and lying and
standing oblongs, consisting of lines of from
2 to 5 lengths.- In order not to repeat the
same form too often, we introduce in Pigs.
2 1 — 3 1 a series of less simple ; containing,
however, the fundamental forms, showing in
the meantime the combination of lines of
various dimensions.
In a similar way, the oblique line is now
introduced and employed. The child pricks
it in various directions, commencing with a
one length line, (Figs. 32 — 35,) combines it to
angles, (Figs. 36 — 39,) the combination of
which will again result in many beautiful
forms. Then follows the perforating of ob-
lique lines of from 2 to 5 lengths, (a single
length containing up to seven points,) which
are employed for the representation of bor-
ders, corner ornaments, etc., (Figs. 42 — 45,
61.) The oblique of the second degree is
also introduced, as shown in Figs. 46 and 47,
and the peculiar formations in Figs. 48 — 51.
Finally, the combination of the oblique
with the perpendicular line, (Figs. 52 and 54,)
and with the horizontal, (Figs. 53 and 55,) or
with both at the same time, (Figs. 56 — 60,)
takes place. The conclusion is arrived at in
the circle (Fig. 62) and the half circle (Figs.
63-69.)
All these elements may be combined in
the most manifold manner, and the inventive
activity of the pupil will find a large field in
producing samples of borders, corner-pieces,
frames, reading marks, etc., etc.
When it is intended to produce amything of
a more complicated nature, the pattern should
be drafted by pupil or teacher upon the net
paper previous to pricking. In such cases,
it is advisable and productive of pleasure to
the pupils, if beneath the perforating paper
another one doubly folded is laid, to have the
pattern transferred by perforation upon this
paper in various copies. Such little produc-
tions may be used for various purposes, and
be presented by the children to their friends
on many occasions. To assist the pupils in
this respect, it is recommended that simple
drawings be placed in the hands of the pupils,
which, owing to their little ability, they cer-
tainly could not yet produce by drawing, but
which they can well trace with their per-
forating tool. These drawings should repre-
sent objects from the animal and vegetable
kingdoms, and may thus be. of great service
for the mental development of the children.
The slowly and carefully perforated forms
and figures will undoubtedly be more last-
ingly impressed upon the mind and longer
retained by the memory, than if they were
only described or hurriedly looked at. Plate
XLIX. presents a few of such pictures, which
can easily be multiplied.
A particular explanation is required for
Fig. 84, on Plate L. In this figure are con-
tained shaded parts, indicating plastic forms,
which so far have not been introduced, all
previous figures presenting mere outlines to
be perforated. It is supposed to be known
that each prick of the needle causes some-
what of an elevation on the reverse (wrong
side) of the paper. If a number of very fine,
scarcely visible pricks are made around a
certain point, an elevated place will be the
result, so much more observable, the larger
the number of pricks concentrated on the
spot. In this wise it is possible to represent
certain parts of a design as standing out in
relief It is understood that very young chil-
dren could not well succeed in such kind of
work. The older ones find material in Figs.
72, 74 and 76 to try their skill in this direc-
tion, and thereby prepare themselves for fig-
ures like 84.
All figures of Plates XXXIX., XLIL, and
XLIX. may well be used for samples of per-
forating and embroidering.
It should be mentioned that the embroider-
ing does not begin simultaneously with the
GUIDE TO KINDER-GARTNERS.
57
perforating, but only after the children have
acquired considerable skill in the last named
occupation. For purposes of
EMBROIDERING,
The same net paper which was used for e.xer-
cises in perforating may be employed, by fill-
ing out the intervals between the holes with
threads of colored silk or worsted. It will be
sufficient for this purpose to combine the
points of one net square only, because other-
wise the stitches would become too short to
be made wilh the embroideiy needle in the
hands of children yet unskilled. For work, to
be prepared for a special purpose, the perfor-
ated pattern should be transferred upon stiff
paper or bristol-board.
Course of instruction just the same as with
perforating.
Experience will show that of the figures
contained on our plates, some are more fit for
perforating, others better adapted for embroid-
ering. Either occupation leads to peculiar
results. Figures in which strongly rounded
lines predominate may be easily perforated,
but with difficulty, or not at all be embroid-
ered, as Figs. 75 and 77. By the process of
embroidering, however, plain forms, as stars,
and rosettes, are easily produced, which could
hardly be represented, or, at best, very imper-
fectly only, by the perforating needle. Figs.
87 — 92, and Fig. 39 on Plate XLII. are ex-
amples of this kind.
To develop the sense of color in the chil-
dren, the paper on which they embroider,
should be of all the various shades and hues,
through the whole scale of colors. If the
paper is gray, blue, black, or green, let the
worsted or silk be of a rose color, white, or-
ange or red, and if the pupil is far enough
advanced to represent objects of nature, as
fruit, leaves, plants, or animals, it will be very
proper to use in embroidering, the colors
shown by these natural objects. Much can
be thereby accomplished toward an early de-
velopment of appreciation and knowledge of
color, in which grown people, in all countries
are often sadly deficient. It has appeared to
some, as if this occupation is less useful than
pleasurable. Let them consider that the ordi-
nary seeing of objects already is a difficult
matter, nay, really an art, needing long prac-
tice. Much more difficult and requiring much
more careful exercise, is a true and correct
perception of color.
If the bcatttifid is introduced at all as a
means of education — and in Froebel's institu-
tions it occupies a prominent place — it should
approach the child in various ways ; not only
mform, but in color, and tone also. To insure
the desired result in this direction, we begin
in the Kinder-Garten, where we can much
more readily make impressions upon the
blank minds of children, than at a later pe-
riod when other influences have polluted their
tastes.
For this reason, we go still another step
farther, and give the more developed pupil a
box with the three fundamental colors, show-
ing him their use, in covering the perforated
outlines of objects with the paint. Children
like to occupy themselves in this manner, and
show an increased interest, if they first pro-
duce the drawing and are subsequently al-
lowed to use the brush for further beautifying
their work.
We only give three fundamental colors, in
order not to confound the beginner by need-
less multiplicity, as also to teach how the sec-
ondary colors,may be produced by mixing the
primarj'.
The perforating and embroidering are be-
gun with the children in the Kinder-Garten,
when they have become sufficiently prepared
for the perception of forms by the use of their
building-blocks and staffs.
THE THIRTEENTH GIFT.
MATERIAL FOR CUTTING PAPER AND MOUNTING PIECES TO PRODUCE
FIGURES AND FORMS.
(PLATES
The labor, or occupation alphabet, pre-
sented by Froebel in his system of education,
cannot spare the occupation, now introduced
— the cutting of paper — the transmutation of
the material by division of its parts, notwith-
standing the many apparently well-founded
doubts, whether scissors should be placed into
the hands of the child at such an early age.
It will be well for such doubters to consider :
Firstly, that the scissors which the children
use, have no sharp points, but are rounded at
their ends, by which the possibilities of doing
harm with them are greatly reduced. Sec-
ondly, it is expected that the teacher employs
all possible means to watch and superintend
the children with the utmost care during their
occupation with the scissors. Thirdly, as it
can never be prevented, that, at least, at times
scissors, knives and similar dangerous objects
may fall into the hands of children, it is of
great importance to accustom them to such,
by a regular course of instruction in their use,
which, it may be expected, will certainly do
something to prevent them from illegitimately
applying them for mischievous purposes.
By placing material before them from which
the child produces, by cutting according to
certain laws, highly interesting and beautiful
forms, their desire of destroying with the scis-
sors will soon die out, and they, as well as
their parents, will be spared many an unpleas-
ant experience, incident upon this childish in-
stinct, if it were left entirely unguided.
As material for the cutting, we employ a
square piece of paper of the size of one-six-
teenth sheet, similar to the folding sheet.
Such a sheet is broRen diagonally, (Plate
LXIX., Fig. 5,) the right acute angle placed
upon the left, so as to produce four triangles
resting one upon another. Repeating the same
proceeding, so that by so doing the two upper
triangles will be folded upwards, the lower
ones downwards in the halving line, eight
triangles resting one upon another, will be
produced, which we use as our first funda-
mental form. This fu7ida7nental form is held,
i?i all exercises, so that the open side, where no
plane connects with another is always turned
toivard the left.
In order to accomplish a sufficient exact-
ness in cutting, the uppermost triangle con-.
tains, (or if it does not, is to be provided with)
a kind of net as a guide in cutting. Dotted
lines indicate on our plates this net-work.
The activity itself is regulated according
to the law of opposites. We commence with
the perpendicular cut, come to its opposite,
the horizontal and finally to the mediation of
both, the oblique.
Plates 51 — 53 indicate the abundance of
cuts which may be developed according to
this method, and it is advisable to arrange for
the child a selection of the simpler elements
into a school of cutting.
The following selection presents, almost
always, two opposites and their combination,
or leaves out one of the former, as is the case
with the horizontal cut, wherever it does not
produce anything essentially new.
a. Perpendicular cuts, 2, 3, 4 — 5, 6, 7.
GUIDE TO KINDER- GARTNERS.
59
b. Horizontal cuts, 8, 9— (above ; above
and below).
c. Perpendicular and horizontal, 18, 19,
20 — 21, 22, 23.
d. Oblique cuts, 34, 35—36, 37, 38.
e. Oblique and perpendicular, 51, 52, 53,
—54, 55- 56—58- 59. 60.
/ Oblique and horizontal, 65, 66, 67.
g. Half oblique cuts, where the diagonals
of standing and lying oblongs, formed of two
net squares, serve as guides — 117, 118, 119 —
121, 122, 123 — 125, 126, 127.
Here ends the school of cutting, perse, for
the first fundamental form, the right angled
triangle. The given elements may be com-
bined in the most manifold manner, as this
has been sufficiently carried out in the forms
on our plates.
The fundamental form used for Plates LIV.
and LV. is a six fold equilateml triangle. It
also is produced from the folding sheet, by
breaking it diagonally, halving the middle of
the diagonal, dividing again in three equal
parts the angle situated on this point of halv-
ing. The angles thus produced will be an-
gles of 60 degrees. The leaf is folded in the
legs of these angles by bending the one acute
angle of the original triangle, upwards, the
other downwards. By cutting the protruding
corners, we shall have the desired form of the
si.x fold equilateral triangle, in which the en-
tirely open side serves as basis of the triangle.
The net for guidance is formed by division of
each side in four equal parts, uniting the points
of division of the base, by parallel lines with
the sides, and drawing of a perpendicular
from the upper point of the triangle upon its
base. It is the oblique line, particularly which
is introduced here. The designs and patterns
from 133 — 145, will suffice for this purpose.
The same fundamental form is used for prac-
tising and performing the circular cuts, al-
though the right angular fundamental form
may be used for the same purpose. Both find
their application subsequently, in a sphere of
development only, after the child by means
of the use of the half and whole rines, and
drawing, has become more familiar with the
curved line. These exercises require great
facility in handling the scissors, besides, and
are, therefore, only to be introduced with
children, who have been occupied in this de-
partment quite a while. For such it is a cap-
ital employment, and they will find a rich
field for operation, and produce many an in-
teresting and beautiful form in connection
with it. The course of development is indi-
cated in figures 164 — 172.
After the child has been sufficiently intro-
duced into the cutting school, in the manner
indicated in the above ; after his fantasy
has found a definite guidance in the ever-re-
peated application of the law, which protects
him against unbounded option and choice, it
will be an easy task to him, and a profitable
one, to pass over to free invention, and to
find in it a fountain of enjoyment, ever new,
and inexhaustibly overflowing. To let the
child, entirely without a guide, be the master
of his own free will, and to keep all discipline
out of his way, is one of the most dangerous
and most foolish principles to which a misun-
derstood love of children, alone, could bring
us. This absolute freedom condemns the
children, too soon, to the most insupportable
annoyance. All that is in the child should be
brought out by means of external influence.
To limit this influence as much as possible is not
to suspend it. Froebel has limited it, in a most
admirable way by placing this guidance into the
child itself, as early as possible ; that from one
single incitement issues a number of others,
within the child, by accustoming it to a lawful
and regulated activity from its earliest youth.
With the first perpendicular cut, which we
made into the sheet (Fig. i,) the whole course
of development, as indicated in the series of
figures up to No. 132 is given, and all subse-
quent inventions are but simple, natural com-
binations of the element presented in the
'■^school." Thus a logical connection prevails
in these formations, as among all other means
of education, hardly any but mathematics
may afford.
60
GUIDE TO KINDER- GARTNERS.
Whereas the activity of the cutting itself,
the logical progress in it advances a most
beneficial influence upon the intellect of the
pupil, the results of it will awaken his sense
of beauty, his taste for the symmetrical, his
appreciation of harmony in no less degree.
The simplest cut already yields an abundance
of various figures. If we make as in Fig. 5, Plate
LI., two perpendicular cuts, and unfold all
single parts, we shall have a square with
hollow middle, a small square, and finally the
frame of a square. If we cut according to
Fig. 6, we produce a large octagon, four
small triangles, four strips of paper of a trape
zium form, nine figures altogether.
All these parts are now symmetrically ar-
ranged according to the law: union of op-
posites — here effected by the position or direc-
tion of the parts, relative to the center —
and after they have been arranged in this
manner, the pupils will often express the de-
sire to preserve them in this arrangement.
This natural desire finds its gratification by
MOUNTING THE FIGURES.
As separation always requires its opposite,
uniting, so the cutting requires mounting.
Plates LVI. to LVIII. present some examples
from which the manner in which the results
of the cutting may be applied, can be easily
derived. With the simpler cuts, the clippings
are to be employed, but if a main figure is
complete and in accordance with the claims
of beauty in itself, itwould be foolish to spoil
it, by adding the same.
This occupation, also, can be made sub-
servient to influence the intellectual develop-
ment of the child by requiring it to point
out all manners in which these forms may
be arranged and put together. (Plate LVI.,
Fig- S-)
In order to increase the interest of the chil-
dren, to give a larger scope to their inventive
power, and at the same time, to satisfy their
taste and sense of color, they may have paper
of various colors and be allowed to e.xchange
their productions among one another.
Both these occupations, cutting and mount-
ing, are for Kinder Garten as well as higher
grades of schools. For older pupils, the cut-
ting out of animals, plants and other forms of
life will be of interest, and silhouettes even
may be prepared by the most expert.
It is evident that not only as a 'simple
means of occupation for the children, during
their early life, but as a preparation for many
an occupation in real life, the cutting of paper
and mounting the parts to figures, as intro-
duced here, are of undeniable benefit.
The main object, however, is here, as in all
other occupations in the Kinder-Garten, de-
velopment of the sense of beauty, as a prep-
aration for subsequent performance in and
enjoyment of art.
THE FOURTEENTH GIFT.
MATERIAL FOR BRAIDING OR WEAVING.
(tlates lix. to lx>v.)
Braiding is a favorite occupation of chil-
dren. The child instinctively, as it were, likes
everything contributing to its mental and
bodily development, and few occupations may
claim to accomplish both, better than the oc-
cupation now introduced. It requires great
care, but the three year old child may already
see the result of such care, whereas even from
GUIDE TO KINDER-GARTNERS.
6l
twelve to fourteen years old pupils often have
to combine all their ingenuity and persever-
ance to perform certain more complicated
tasks in the braiding or weaving department.
It does not develop the right hand alone, the
left also finds itself busy most of the time. It
satisfies the taste of color, because to each
piece of braiding, strips of at least two differ-
ent colors belong. It excites the sense of
beauty because beautiful, /. e , symmetrical,
forms are produced ; at least their production
is the aim of this occupation. The sense and
appreciation of number are constantly nour-
ished, nay, it may be asserted, that there is
hardly a better means of affording percep-
tions of numerical conditions, so thorough,
founded on individual experience and ren-
dered more distinct by diversity in form and
color, than '^braiding." The products of the
child's activity, besides, are readily m.ade use-
ful in practical life, affording thereby capital
opportunities for expression of its love and
gratitude, by presents prepared by its own
hand.
The material used for this occupation are
sheets of paper prepared as shown on Plate
LIX., strips of paper, and the braiding needle,
also represented on Plate LIX.
A braid work is produced by drawing with
the needle a loose strip (white) through the
strips of the braiding sheet, (green) so that a
number of the latter will appear over, another
under the loose strip. These numbers are
conditioned by the form the work is to as-
sume. As there are but two possible ways
in which to proceed, either lifting up, or pres-
sing down, the strips of the braiding sheet,
the course to be taken by the loose strip is
easily expressed in a simple formula. All
varieties of patterns are expressible in such
formulas, and therefore easily preserved and
communicated.
The simplest formula of course, is when one
strip is raised and the next pressed down.
We express this formula by i u (up), i d
(down). All such formulas in which only two
figures occur, are called simple formulas ;
combination formulas, however, are such as
contain a combination of two or more such
simple formulas.
But with a single one of such formulas, no
braid work can yet be constructed. If we
should, for instance, repeat with a second,
third, and fourth strip, i u, i d, the loose
strips would slip over one another at the
slightest handling, and the strips of the braid-
ing sheet and the whole work, drop to pieces
if we should cut from it, the margin. In do-
ing the latter, we have, even with the most
perfect braidwork, to employ great care ; but
it is only then a braid or weaving work exi^sts
— when all strips are joined to the whole by
other strips, and none remain entirely de-
tached.
To produce a braid work, we need at least
two formulas, which are introduced alternately.
Proceeding according to the same fundamen-
tal law which has led us thus far in all our
work, we combine first with i ;/, i d, its oppo-
site \ d, \ u.
Such a combination of braiding formulas
by which not merely a single strip, but the
whole braid work, is governed, is a braiding
scheme.
Braiding formulas, according to which the
single strip moves, are easily invented. Even
if one would limit one's self to take up or press
down no more than five strips, (and such a
limitation is necessary, because otherwise the
braiding would become too loose,) the follow-
ing thirty formulas M'ould be the result :
1, lu id 9, 3u id 17, 4u 2d 24, 5d lu
2, id lu 10, 3d lu 18, 4d 2u 25, 5u 2d
3, 2u 2d n, 3u 2d 19, 4U 3d 26, 5d 2u
4, 2d 2u 12, 3d 2u 20, 4d 3u 27, 5u 3d
5, 2u id 13, 4u 4d 21, 5u 5d 28, 5d 3U
6, 2d lu 14, 4d 4u 22, 5d 5u 29, 5U 4d
7, 3u 3d 15, 4U id 23, 5u id 30, 5d 4U
8, 3d 3u 16, 4d lu
From these thirty formulas, among which are
always two oppositionally alike, as for in-
stance, I and 2, 9 and 10, 25 and 26, hun-
dreds of combined, or combination formulas
can be formed by simply uniting two of them.
In the beginning it is advisable to combine
62
GUIDE TO KINDER-GARTNERS.
such as contain equally named numbers either
even or odd. The following are some ex-
amples :
Formulas i and 3, lu id, 2u 2d.
" I and 5, III id, 2u id.
" I and 7, III id, 3U 3d.
" I and 9, lu id, 3U id.
" I and II, lu id, 3U 2d.
" I and 13, III id, 4U 4d.
" I and 15, lu id, 411 id.
" I and 17, lu id, 4U 2d.
" I and 19, lu id, 4U 3d.
" I and 21, lu id, 5U 5d.
" I and 23, lu id, 5U id.
I and 25, III Id, 511 2d.
" I and 27, lu id, 5U 3d.
" I and 29, lu id, 5u 4d.
If we also add the formulas under the even
numbers in the given thirty, we have to read
them inversely. Thus :
Formulas I and 6, lu id, lu 2d.
" I and 10, lu id, lu 3d.
" I and 12, III id, 2u 3d.
" I and 16, lu id, lu 4d.
" I and iS, lu id, 2u 4d.
" I and 20, ui id, 3U 4d.
" I and 24, III id, lu 5d.
" I and 26, lu id, 2u 5d.
I and 28, lu id, 3U 5d.
" I and 30, lu id, 4U 5d.
By a combination of one single formula
with the twenty-four others, we receive new
combination formulas and see that inventing
formulas is a simple mathematical operation,
regulated by the laws of combination.
Much more difficult it is to invent braiding
schemes. Not to dwell too long on this point,
we introduce the reader to the course shown
in pictures on our plates, which is arranged so
systematically that either as a whole or with
some omissions, it may be worked through
with children from three to six years, as a
braiding school. It begins with simple formu-
las and by means of the law of oppbsites is
carried out to the most beautiful figures.
Formula i, lu id, (Fig. i,) is first intro-
duced; opposite in regard to number is 2u
2d, (Fig. 2). In Fig. 3 the numbers i and 2
are combined ; Fig. 4 is a combination of
Figs. I and 2 ; Fig. 5 a combination of Figs.
I and 3 by combining the simple formulas.
If we examine Fig. 5, the number 3 makes
itself prominent in the strips running ob-
liquely. In Fig. 6 it occurs independently as
opposite to I and 2, and then follows in Figs.
7-15 a series of mediative forms all uniting
the opposites in regard to number. In all
these patterns the squares or oblongs pro-
duced, are arranged perpendicularly under, or
horizontally beside, one another. Except in
Fig. I, the oblique line appears already be-
side the horizontal and perpendicular. Thus,
this given opposite of form is prevailing on
Plate LXL, and we apply here the same for-
mulas as on Plate LX., with the difference,
however, that we need only one formula,
which in the second, third strip, etc], always
begins one strip later or earlier. Thus in
Fig. 16, the formula 2U 2d (as in Fig. 2) is
carried out. The dark and light strips of the
pattern run here from right above to left be- •
low. Opposite of positioji to Fig. 16, is
shown in Fig. 17, where both run the oppo-
site way. Fig. 18 shows combination, and
Fig. 19 double combination. In opposition
to the connected oblique lines, the broken line
appears in Fig. 20. As the formula 2U 2d
has furnished us five patterns, so the formula
of Fig. 3, lu 2d, furnishes the series 21 — 25.
Nos. 21 and 22 are opposites as to direction.
Fig. 23 shows the combination of these op-
posites. Figs. 24 and 25, opposites to one
another, are forms of mediation between 21
and 22. With them for the first time a mid-
dle presents itself.
While in Figs. 21 — 26 the dark color is
prevailing. Figs. 26 — 28 show us predom-
inantly, the light strip, consequently the op-
posite in color. In 29 — 32, formulas from Figs.
3 — 5 are employed. Fig. 29 requires an op-
posite of direction, a pattern in which the strips
run from left above to right below. Fig. 30
gives the combination of both directions and
Figs. 31 and 32 are at the same time op-
posites as to direction and color.
It is obvious that each single formula can
be used for a whole series of divers patterns,
GUIDE TO KINDER-GARTNERS.
63
and the invention of these patterns is so easy
that it will suffice if we introduce each new
formula very briefly. •
Fig- 33 's a form of mediation for the for-
• mula 3U 3d ; Fig. 34 shows a different appli-
cation of the same formula. In Fig. 35 the
broken line appears again, but in opposition
to 20, it changes its direction with each break.
In Figs. 36 — 40 the formulas of Figs. 7, 8,
10, II, and 13 are carried out. The braiding
school, J>er se, is here concluded. Whoever
may think it too extensive may select from it
Nos. I, 2, 3, 6, 7, 10, 16, 17, 18, 21, 26, 24,
25, 33, and 34.
But if any one would like still to enlarge
upon it, she may do so by working out, for
each single formula the forms or patterns
16, 17, 18, 19, 24 and 25, and continue the
school to the number 5. The number of pat-
terns will be made, thereby, ten times larger.
Another change, and enlargement of the
school may be introduced by cutting the
braiding strips, as well as those of the braiding
sheet, of different widths. We can, thereby,
represent quite a number of patterns after
the same formula, which are, however, essen-
tially different. This is particularly to be
recommended with very small children, who
necessarily will have to be occupied longer
with the simple formula lu id. But for more
developed braiders, such change is of interest,
because by it a great variety of forms may
be produced which may be rendered still
more interesting and attractive, by a variety
of colors in the loose braiding strips.
With patterns that have a middle, as 24
and 28, it is advisable to let the braiding be-
gin (especially with beginners,) with the mid-
dle strip, and then to insert always one strip
above, and one below it.
It is not unavoidably necessary that the
school should be finished from beginning to
end, as given here. Quite the reverse. The
pupil, after having successfully produced some
patterns, may be afforded an opportunity for
developing his skill by his own invention, in
trying to form, by braiding a cross, with hol-
low middle, (Fig. 41,) a standing oblong, (42,)
a long cross, (43,) a small window, (45,) etc.
Plate LXIIL, presents some patterns which
may be used for wall-baskets, lamp tidies,
book-marks, etc., and which may easily be
augmented by such as have acquired more
than ordinary skill.
Finally, Plate LXIV. shows in figures i — 3,
obliquely intertwined strips, representing the
so called free-braiding, the braiding without
braiding sheet. This is done in the following
manner : Cut two or more long strips (Fig. 4)
of a quarter sheet of colored paper, (green,)
and fold to half their length, (Fig. 5,) cut
then, of differently colored paper, (white,)
shorter strips, afso fold these to half their
length. Put the green strips side by side of
one another, as shown in Fig. 7, so that the
closed end of the one strip lies above, and
that of the other below, (7^^.) Then take
the white strip, bend it around strip i, and
lead it through strip 2, (Fig. 8.) The second
strip is applied in an opposite way, laying it
around 2, and leading it through i. Em-
ploying four instead of two green strips, the
bookmark. Fig. 9, will be the result. The
protruding ends are either cut or scolloped.
By introducing strips of different widths,
a variety of patterns can also here be pro-
duced.
Instead of paper, glazed muslin, leather,
silk or woolen ribbon, straw and the like may
be used as material for braiding.
THE FIFTEENTH GIFT.
THE INTERLACING SLATS.
(plates lxv. and lxvi.)
Froebel, in his Gifts of the Kinder-Garten,
does not present anything perfectly new. All
his means of occupation are the result of care-
ful observation of the playing child. But he
has united them in one corresponding whole ;
he has invented a method, and by this method
presented the possibility of producing an ex-
haustless treasure of formations which, each
influencing the mind of the pupil in its pecu-
liar way, effect a development most harmoni-
ous and thorough of all the mental faculties.
The use of slats for interlacing is an occupa-
tion already known to our ancestors, and who
has not practiced it to some extent in the
days of childhood ? But who has ever suc-
ceeded in producing more than five or six
figures with them ? Who has ever derived,
from such occupation, the least degree of that
manual dexterity and mental development,
inventive power and talent of combination,
which it affords the pupils of the Kinder-Gar-
ten, since Froebel's method has been applied
to the material ?
Our slats, ten inches long, three-eighths of
an inch broad and one-sixteenth of an inch
thick, are made of birch or any tough wood,
and a dozen of them are sufficient to produce
quite a variety of figures. They form, as it
were the transition from the plane of the tab-
let to the line of the staffs, (Ninth Gift) differ-
ing, however, from both, in the fact that forms
produced by them are not bound to the plane,
but contain in themselves a sufficient hold to
be separated from it.
The child first receives one single slat. Ex-
amining it, it perceives that it is flexible, that
its length surpasses its breadth many times,
and again that its thickness is many times
less than its breadth.
Can the pupil name some objects between
which and the slat, there is any similarity ?
The rafters under the roof of a house, and
in the arms of a wind-mill, and the laths of
which fences, and certain kinds of gates, and
lattice work are made, are similar to the slat.
The child ascertains that the slat has two
long plane sides and two ends. It finds its
middle or center point, can indicate .the upper
and lower side of the. slat, its upper and lower
end, and its right and left side. After these
preliminaries, a second slat is given the child.
On comparison the child finds them perfectly
alike, and it is then led to find the positions
which the two slats may occupy to each other.
They can be laid parallel with each other, so
as to touch one another with the whole length
of their sides, or they may not touch at all.
They can be placed in such positions that
their ends touch in various ways, and can be
laid crosswise, over or under one another.
With an additional slat, the child now con-
tinues these experiments. It can lay various
figures with them, but there is no binding or
connecting hold. Therefore as soon as it at-
tempts to lift its work from the table, it falls
to pieces.
By the use oifour slats, it becomes enabled
to produce something of a connected whole,
but this only is done, when each single slat
coines in contact with at least three other slats.
GUIDE TO KINDER-GARTNERS.
65
Two of these should be on one side, the third
or middle one should rest on the other side
of the connecting slat, so that here again the
law of opposites and their mediation is fol-
lowed and practically demonstrated in every
figure.
It is not easy to apply this law constantly
in the most appropriate manner. But this
ver}' necessity of painstaking, and the reason-
ing, without which little success will be at-
tained, is productive of rich fruit in the de-
velopment of the pupil.
The child now places the slat aa horizon-
tally upon the table. £b is placed across it
in a perpendicular direction ; cc in a. slanting
direction under a and b, and eld is shoved under
aa and over bb and under cc, as shown in Fig. i.
This gives a connected form, which will not
easily drop apart. The child investigates
how each single slat is held and supported —
it indicates the angles, which were created,
and the figures which are bounded by the va-
rious parts of the slats.
To show how rich and manifold the material
for obse'rvation and instruction given in this
one figure is, we will mention that it contains
twenty-four angles, of which 8 (i — 8) are
right, 8 (9 — 16) acute, and 8 (17 — 24) obtuse
— formed by one perpendicular slat, bb, one
horizontal, aa, one slanting from left above
to right below, cc, and another slanting from
right above to left below, dd.
Each single slat touches each other slat
once ; two of them, aa and bb, pass over two
and under one, and the others, cc and dd, pass
under two and over one of the other slats, by
which interlacing, three small figures are
formed within the large figure, one of which
is a figure with two right, one obtuse and one
acute angle, (3, 6, 22, 10), and four unequal
sides, and two others, one of which is a right
angled triangle with two equal sides, and the
other is a right angled triangle with no equal
sides.
By drawing the slats of Fig. i apart. Fig.
2, an acute angled triangle is produced — by
drawing them together, Fig. 3 results, from
which the acute angled triangle, Fig. 4, can
again be easily formed. Each of these fig-
ures present? abundant matter for* investiga-
tion and instructive conversation, as shown
above in connection with Fig. i.
The child now receives a fifth slat. Sup-
pose we have Fig. 2, consisting of four slats
— ready before us — we can, by adding the
fifth slat, easily produce what appears on
Plate LXV. as Fig. 8.
If the five slats are disconnected, the child
may lay two, perpendicularly at some distance
from each other, a third in a slanting position
over them from right above to left below, and
a fourth in an opposite direction, v.heu the
two latter will cross each other in their mid-
dle. By means of the fifth slat the interlac-
ing then is carried out, by sliding it from
right to left under the perpendicular over the
crossing two, and again under the other perpen-
dicular slat, and thereby the figure 5 made firm.
By bending the perpendicular slats together.
Fig. 6 is produced; when the horizontal slat
assumes a higher position, a five angled fig-
ure appears — one of the slanting slats, how-
ever, has to change its position also, as shown
in Fig. 7. In Fig. 8, the horizontal slat is
moved downward. In Fig. 9, the original
position of the crossing slats is changed ; in
the triangle. Fig. lo, still more, and in Figs.
II and 12, other changes of these slats are
introduced.
The addition of a sixth slat enables us still
further to form other figures from the previous
ones — Fig. 17 can be produced from 9, 18
from 10 or 11, 22 from 12, and then a fol-
lowing series can be obtained by drawing
apart and shoving together as heretofore.
Let us begin thus : the child lays (Fig. 13)
two slats horizontally upon the table — two
slats perpendicularly over them ; a large
square is produced. A fifth slat horizontally
across the middle of the two perpendicular
slats, gives two parallelograms, and by con-
necting the si.xth slat from above to below with
the three horizontal slats, so that the middle
one is under and the two outside slats over it,
66
GUIDE TO KINDER-GARTNERS.
the child will have formed four small squares,
of equal size.
The figures 17 and 18, (triangles,) and 19
and 23, (hexagons,) deserve particular atten-
tion, because they afford valuable means for
mathematical observations.
On Plate LXVI. we find some few ex-
amples of seven intertwined slats, (Figs. 25 —
28,) of eight slats, (Figs. 29 — 36,) of nine slats,
(Figs. 37 — 40,) and often slats, (Figs. 41 — 43.)
All we have given in the above are mere
hints to enable the teacher and pupil to find
more readily by individual application, the
richness of figures to be formed with this oc-
cupation material.
It is particularly mathematical forms, reg-
ular polygons, (Figs. 28, 31, 40, 42,) contem-
plation of divisions, produced by diagonals,
etc., planes and proportions of form, which,
informs of knowledge, are brought before the
eye of the pupil, with great clearness and dis-
tinctness, by the interlacing slats.
In the meantime, it will afford pleasure to
behold the forms of beauty, as given in Figs.
3°) 33; 37; nor should \\i^ forms of life be
forgotten, as they are easily produced by a
larger number of slats, (Fig. 39 — a fan ; 35
and 36 — fences,) by combining the work of
several pupils.
The figures are not simply to be constructed
and to be changed to others, but each of them
is to be submitted to a careful investigation
by the child, as to its angles, its constituent
parts, and their qualities, and the service each
individual slat performs in the figure as indi-
cated with Fig. I, on page LXV.
The occupation with this material will fre-
quently prove perplexing and troublesome
to the pupil ; oftentimes he will try in vain
to represent the object in his mind.
Having almost successfully accomplished
the task, one of the slats will glide out from
his structure, and the whole will be a mass
of ruins. It was the one slat, which, owing to
its dereliction in performing its duty, des-
troyed the figure, and prevented all the others
from performing theirs.
It will not be difficult for the thinking
teacher to derive from such an occurrence,
the opportunity to make an application to
other conditions in life, even within the sphere
of the young child, and its companions in and
out of school. The character of this occu-
pation does not admit of its introduction be-
fore the pupils have spent a considerable time
in the Kinder-Garten, in which it is only be-
gun, and continued in the primary depart-
ment.
THE SIXTEENTH GIFT.
THE SLAT WITH MANY LINKS.
This occupation material, which may be
used at almost any grade of development in
the Kinder Garten, the primary and higher
school departments, is so rich in its applica-
tions, that we cannot attempt to describe it
extensively, nor give illustrations of the vari-
ous ways in which it can be rendered useful.
Suffice it to say, that it may be employed in
representing all various kinds of lines, angles
and mathematical figures, and that even forms
of life and beauty may be presented by it.
We have slats with 4, 6, 8 and 16 links,
which are introduced one after the other when
opportunities offer. In placing the first. into
the hand of the child, we would ask him to
unfold all the links of the slat, and to place
it upon the table so as to represent a perpen-
dicular, horizontal, and then an oblique line.
GUIDE TO KINDER-GARTNERS.
67
By bending two of the links perpendicularly,
and the two others horizontally, we form a
right angle. Bending one of the legs of the
angle toward, or from the other, we receive
the acute and obtuse angles, which grow
smaller or larger, the nearer or farther the
legs are brought to, or from each other, until
we reduce the angles to either a perpendicular
line of two links' length, or a horizontal line
of the length of four links.
We may then form a square. Pushing two
opposite corners of it toward each other, and
bending the first link so as to cover with
it the second, and, by then joining the
end of the fourth link to where the first
and second are united, we shall form an
equilateral triangle. (Which other triangle
can be formed with this slat, and how ?)
The capital letters V, W, N, M, Z, and the
figure 4 can be easily produced by the chil-
dren, and many figures be constructed by the
teacher in which the pupils may designate the
number and kinds of angles, which they con-
tain, as is done with the movable slats on
other occasions.
The slats with 6, 8 and 16 links, to be
introduced one after the other, if used
in the manner here indicated, can be ren-
dered exceedingly interesting and instruct-
ive to the pupils. Their ingenuity and in-
ventive power will find a large field in the
occupation with this material if, at times,
they are allowed to produce figures them-
selves, of which the more advanced pupils
may make drawings and give a description
of each orally.
It would be needless to enlarge here upon
the richness of material afforded by this gift,
as half an hour's study of and practice with it
will convince each thinking teacher fully of
the treasure in her hand and certainly make
her admire it on account of the simplicit)' of
its application for educational purposes in
school and family.
THE SEVENTEENTH GIFT.
MATERIAL FOR INTERTWINING.
(PLATES LXVII., LXVIII.)
Intertwining is an occupation similar to
that of interlacing. Aim of both is repre-
sentation of plane — outlines. In the occupa-
tion with the interlacing slats we produced
forms, which were to be destroyed again, or
whose peculiarities, at least, had to be changed
to produce something new ; here, we produce
permanent results. There, the material was
in everj' respect a ready one ; here, the pupil
has to prepare it himself There, hard slats
of little flexibility ; here, soft paper, easily
changed. There, production of purely math-
ematical forms by carefully employing a given
material ; here, production of similar forms
by changing the material, which forms, how-
ever, are forms of beauty.
The paper strips, not used when preparing
the folding-sheets, are used as material, adapted
for the present occupation. They are strips
of white or colored paper, from eight to ten
inches long and varying in breadth. Each
strip is subdivided in smaller strips of three-
quarters of an inch wide, which by folding
their long sides are transformed to threefold
strips of eight to ten inches long and one-
quarter of an inch wide.
The children will not succeed well, in form-
ing regular figures from these strips at first.
GUIDE TO KINDER-GARTNERS.
As the main object of tliis occupation is to
accustom the child to a clean, neat and cor-
rect performance of his task, some of the
tablets of Gift Seven are given him as pat-
terns to assist liim ; or the child is led to draw
on his slate the three, four, or many cornered
forms, and to intertwine his paper strips ac-
cording to these.
First, a right angled isosceles triangle is used
for laying around it one of these strips so as
to enclose it entirely. We begin with the left
cathetus, put the tablet upon the strip, folding
it toward the right over the right angle. The
break of the paper is well to be pressed down,
and then the strip is again folded around the
acute angle toward the left. Where the hy-
potenuse (large side) touches the left cathetus
(small side), the strip is cut and the ends of
the figure there closed by gluing them to-
gether by some clean adhesive matter. Care
should be taken that the one end of each side
be under, the other over, that of the other.
Thus the various kinds of triangles, (Figs.
I — 3,) squares, rhombus, rhomboids, etc., are
produced.
Two like figures are combined, as shown in
Figs. 4 — 6. If strips prove to be too short,
the child is shown how to glue them together,
to procure material for larger and more com-
plicated forms. Thus, it produces, with one
long strip. Figs. i6, i8, 19, 20; with two long
strips. Figs. 17, 21. Fig. 22 shows the natu-
ral size ; all others are drawn on a somewhat
reduced scale. It cannot be difficult to pro-
duce a great variety of similar figures, if one
will act according to the motives obtained with
and derived from the occupation with the in-
terlacing slats.
This occupation admits of still another and
very beautiful modification, by not only pinch-
ing and pressing the strip where it forms
angles, but by folding it to a rosette. This
process is illustrated in Figs. 7 — 9. The strip
is first pinched toward the right, (Fig. 7,) then
follows the second pinch downward, (Fig. 8,)
then a third toward the left, when the one end
of the strip is pushed through under the other,
(Fig- 9-)
Here, also, simple triangles, squares, pen-
tagons and hexagons are to be formed, then
two like figures combined, and finally more
complicated figures produced. (Compare ex-
amples given in Figs. 10 — 15.)
Whatever issues from the child's hand suffi-
ciently neat and clean and carefully wrought,
may be mounted on stiff paper or bristol
board, and disposed of in many ways.
The occupation of intertwining shows
plainly how by combination of simple mathe-
matical forms, forms of beauty may be pro-
duced. These latter should predominate in
the Kinder-Garten, and the mathematical are
of importance as they present the elements for
their construction. The mathematical ele-
ment of all our occupations is in so far of
significance, as the child receives from it
impressions of form ; but of much more im-
portance is the development of the child's
taste for the beautiful, because with it, the
idea of the good is developed in the mean-
time.
As the various performances of this occu-
pation, cutting, folding and mounting, require
a somewhat skilled hand, it is introduced
in the upper section of the Kinder-Garten
only.
THE EIGHTEENTH GIFT.
MATERIAL FOR PAPER- FOLDING.
(plates lxix. to lxxi.)
Froebel's sheet of paper for folding, the
simplest and cheapest of all materials of oc-
cupation, contains within it a great multitude
of instructive and interesting forms. Almost
every feature of mathematical perceptions, ob-
tained by means of previous occupations, we
again find in the occupation of paper-folding.
It is indeed a compendium of elementary
mathematics, and has, therefore, very justly
and judiciously been recommended as a use-
ful help in the teaching of this science in
public schools.
Lines, angles, figures, and forms of all
varieties appear before us, after a few mo-
ments' occupation with this material. The
multitude of impressions, however, should
not misguide us ; and we should always, and
more particularly in this work, be careful to
accompany the work of the children with nec-
essarj' conversation and pleasant entertain-
ment, for the relief of their young minds.
We prepare the paper for folding in the fol-
lowing manner :
Take half a sheet of letter paper, place it
upon the table in such a manner as to have
the longest sides extend from left to right.
Then halve it by covering the upper corners
with the lower ones, (Fig. i.) Then turn the
now left and right upper (previously lower)
corners back, towards the center ; invert the
paper ; turn also the two other corners toward
the center, and then we have the form of a
trapezium, (Fig. 2.) Unfolding the sheet at
its base line, a hexagon, (Fig. 3,) will show
itself; in which we obsen'e four triangles, of
which two and two lie together, forming a
larger triangle. At the base lines of these
larger triangles, the sheet is again folded, and
neatly and accurately cut, severing thereby
the two large double, lying triangles from the
single and oblong strips of paper.
Each of these triangles we cut through
from where the sides of the small triangles
touch each other, unfold the small triangles,
and we now have four square pieces, and one
oblong piece of paper, (Fig. 4.) The former
w^e employ for folding, the latter we keep for
future use, in the occupations of intertwining,
braiding, or weaving.
The child should be accustomed to ±e
strictest care and cleanliness in the cutting as
well as the folding.
This is necessary, because paper carelessly
folded and cut, will not only render more
difficult every following task, nay, make im-
possible ever}' satisfactory result ; especially,
should this be the case, because, we do
not intend simply to while away our own
and the child's precious time, but are en-
gaged in an occupation whose final aim is
acquisition of ability to work, and to work
well — one of the most important claims
hum.in society is entitled to make upon each
individual.
The child prepares for himself, in the man-
ner described, a number of folding sheets,
and submits them to a series of regular
changes, by bending and folding, in conse-
quence of which the fundamental forms are
produced, from w^hich sequels of forms of
^o
GUIDE TO KINDER-GARTNERS.
life and beauty are subseqently developed,
by means of the law of opposites.
On the road to this goal, a surprising num-
ber of forms of knowledge present them- ,
selves.
The sheet is now folded once more, fol-
lowing the diagonal, (Fig. 5,) and will then
present, when unfolded, the division of the
square, in two right-angled isosceles triangles.
Folded once more according to the other
diagonal, (Fig. 6,) and again unfolded, we find
each of the large triangles, halved by a per-
pendicular, (Fig. 7.) Now the lower corner
is bent upon the left, and the right one upon
the upper, and the sheet is so folded, that it
is divided into equal oblong halves by a
transversal. The same is done to the op-
posite transversal, and we have the Fig. 9,
affording a multitude of mathematical object
perceptions.
If we now take the lower corner, (Fig. 9,)
bend it exactly toward the center of the sheet
and fold it, the pentagon, (Fig. 10,) will be the
result. We fold the opposite corner in like
manner and produce the hexagon, (Fig. 11,)
and finally with the two remaining corners,
Fig. 12" is formed containing four triangles,
touching one another with their free sides,
each of them again showing a line halving
them in two equal triangles.
If we invert 12% we have 12'', a connected
square, in which the outlines of eight congru-
ent triangles appear. If 12° is unfolded we
shall see beside a multiplication of previous
forms, parallelograms also. If we start from
12°, fold the corners toward the middle, (Fig.
15,) we shall receive a form consisting of
double layers of paper, and showing four tri-
angles, under which again, four separate
squares are found. This is the fundamental
form for a series of forms of life, (Fig. 16.)
It is utterly impossible to give a minute de-
scription how forms of life may be produced
from this fundamental form. Practical at-
tempts and occasional observation in the
Kinder-Garten will be of more assistance tljan
the most detailed illustrations and descrip-
tions. Froebel's Manual mentions, among
others, the following objects : A table-cloth
with four hanging corners, a bird, a sail boat,
a double canoe, a salt-cellar, flower, chemise,
kite, wind-mill, table, cigar-holder, flower-pot,
looking glass, boat with seats, etc. Still richer
become the forms of life, if we bend the cor-
ners of the described fundamental form, once
more toward the middle. In connection with
this, the manual mentions the following forms :
the knitting-pouch, the chest of drawers, the
boots, the hat, the cross, the pantaloons, the
frame, the gondola, etc. For the construction
of these forms, it is advisable to use a larger
sheet of paper, perhaps half a sheet of letter
paper.
But the simple fundamental form, for the
forms of life, is also the fundamental form for
the forms of beauty, contained on Plate LXX.,
(Fig. 16.) Unfold the fundamental form, do
not press the corners but first the middle of
the upper and lower side, then the two other
sides toward the middle of the sheet, and the
double canoe will be the result, (hexagon with
two long and four short sides.) If the over-
reaching triangles are now bent back toward
the middle. Fig. 17 appears, from which, up
to Fig. 21, the following forms are easily con-
structed according to the law of opposites.
From quite a similar fundamental form, the
series 22 — 27 originates.
If we finally take the sheet as represented,
in 12'' fold the lower right corner toward the
middle, also the left upper, (Fig. 13,) also the
two remaining corners, we shall have four
triangles, consisting of a double layer of pa-
per which may be lifted up from the square
ground and which upper layer again is divi-
ded in two triangles, (Fig. 14.)
Invert this figure and you will have Fig. 28,
four single squares, the fundamental form of
a series of forms of beauty on Plate LXXI. ;
the latter easily to be derived from this former,
under the guidance of the well known law of
opposites.
The hints given in the above might be aug-
mented to a considerable extent and still not
GUIDE TO KINDER-GARTNERS.
71
exhaust the matter. They are given espe-
cially to stimulate teacher and child to indi-
vidual practical attempts in producing forms
by folding. The best results of their activity
can be improved by cutting out or coloring,
which adds a new and interesting change to
this occupation. A change of the fundamental
form in three directions yields various series
of forms of beautj', which may be multi-
plied ad infinitum. Thereby, not only the idea
of sequel in representations is given, but also
the understanding unlocked for the various
orders in nature.
Furthermore, this occupation gives the pu-
pil such manual dexterity as scarcely any
other does, and prepares the way to various
female occupations, besides being immediately
preparatory to all plastic work. Early training
in cleanliness and care is also one of the re-
sults of a protracted use of the folding sheet.
It is evident that only those children who
have been a good while in the Kinder-Garten,
can be employed in this department of occu-
pation. The peculiar fitness of the folding
sheet for mathematical instruction beyond the
Kinder-Garten, must be apparent after we
have shown how useful it can be made in this
institution.
THE NINETEENTH GIFT.
MATERIAL FOR PEAS-WORK.
(plates lxxii. and lxxiii.)
We have already tried, in connection with
the Ninth Gift, (the laying staffs,) to render
permanent the productions of the pupils, by
stitching or pasting them to stiff paper. We
satisfied, by so doing, a desire of the child,
which grows stronger, as the child grows
older — the desire to produce by his own activ-
ity certain lasting results. It is no longer the
incipient instinct of activity which governs
the child, the instinct which prompted it, ap-
parently without aim, to destroy everything
and to reconstruct in order to again de-
stroy. A higher pleasure of production has
taken its place ; not satisfied by mere doing,
but requiring for its satisfaction also delight
in the created object — if even unconsciously —
the delight of progress, which manifests itself
in the production, and which can be observed
only in and by the permanency of the object
which enables us to compare it with objects
previously produced.
To satisfy the claims of the pupil in this
direction in a high degree, the working with
peas is eminently fitted, although considerable
manual skill is required for it, not to be ex-
pected in any child before the fifth year. The
material consists of pieces of wire of the thick-
ness of a hair-pin, of various sizes in length,
and pointed at the ends. They again represent
lines. As means of combination, as embodied
points of junction, peas are used, soaked about
twelve hours in water and dried one hour pre-
vious to being used. They are then just soft
enough to allow the child to introduce the
points of the wires into them, and also hard
enough to afford a sufficient hold to the latter.
The first exercise is to combine two wires,
by means of one pea, into a straight line, an
obtuse, right, and acute angle. What has been
said in regard to laying of staffs in connection
with Fig. I — 23 on Plate XXX. will sen'e
here also.
Of three wires, a longer line is formed ;
angles, with one long, and one short side.
72
GUIDE TO KINDER- GARTNERS.
The three wires are introduced into one pea,
so that they meet in one point ; two parallel
lines may be continued by a third ; finally the
equilateral triangle is produced.
Then follows the square, parallelogram,
rhomboid ; diagonals may be drawn and the
forms shown on Plate LXXIL, figures i — lo,
be produced. The possibility of representing
the most manifold forms of knowledge, of life
and of beauty, is reached, and the forms pro-
duced may be used for other purposes. The
child may produce six triangles of equal size,
and repeat with them all the exercises, gone
through with the tablets, and may enlarge
upon them.
Or the child may prepare 4, 8, 16 right an-
gled triangles, or obtuse angled, or acute an-
gled triangles and lay with them the figures
given on Plate LXXIL, etc., for the course of
drawing, and carry them out still further.
After these hints it seems impossible not
to occupy the child in an interesting and in-
structive manner.
But the condition attached to each new Gift
of the Kinder-Garten is some special progress
in its course.
We produced outlines of many objects with
the staffs ; all formations, however, remained
planes, whose sides were represented by staffs.
In the working with peas, the wires represent
edges, the peas serve as corners, and these
skeleton bodies are so much more instructive
as they allow the observation of the outer
forms in their outlines, and the inner structure
and being of the body at the same time.
The child unites two equilateral triangles
by three equally long wires, and forms thereby
a prism, (Fig. 14;) four equilateral triangles,
give the three-sided pyramid ; eight of them,
the octahedron. (Figs. 15 and 16.)
From two equal squares, united by four
wires of the length of the sides, the skele-
ton cube. Fig. 17, is formed; if the uniting
wires are longer than the sides of the square,
the four-sided column (Fig. 8); is one of the
squares larger than the other, a topless pyra-
mid will be produced, etc.
It is hardly possible that pupils of the
KinderGarten should make any further prog-
ress in the formation of these mathematical
forms of crystallization, as the representation
of the many-sided bodies, and especially the
development of one from another, requires
greater care and skill than should be expected
at such an early period of life. It will be re-
served for the primary, and even a higher
grade of school, to proceed farther on the
road indicated, and in this manner prepare
the pupil for a clear understanding of regular
bodies. (Fig. 19 shows how the octahedron
is contained in the cube.)
This, however, does not exclude the con-
struction by the more advanced pupils of the
Kinder-Garten, of simple objects, in their
surroundings, such as benches, (Fig. 21,)
chairs, (Fig. 23,) baskets, etc., or to try to
invent other objects.
Whoever has himself tried peas-work, will
be convinced of its utility. Great care, much
patience, are needed to produce a somewhat
complicated object ; but a successful structure
repays the child for all painstaking and per-
severance. By this exercise, the pupils im-
prove in readiness of construction, and this
is an important preparation for organiza-
tion.
More advanced pupils try also, successi.-
fully, to construct letters and numerals, with
the material of this Gift.
The bodies produced by peas-work may
be used as models in the modeling depart-
ment. The one occupation is the comple-
ment of the other. The skeleton cube allows
the observation of the qualities of the solid
cube, in greater distinctness. The image of
the body becomes in this manner more per-
fect and clear, and above all, the child is
led upon the road, on which alone it is
enabled to come into possession of a true
knowledge and correct estimate of things;
the road on which it learns, not only to ob-
serve the external appearance of things, but
in the meantime, and always, to look at their
internal being.
THE TWENTIETH GIFT.
MATERIAL FOR MODELING.
(plate lxxiv.)
Modeling, or working in clay, held in high
estimation by Froebel, as an essential part of
the whole of his means of education is, strange
to say, much neglected in the Kinder-Garten.
As the main objection to it named is that the
children, even with the greatest care, can not
prevent occasionally soiling their hands and
their clothes. Others, again, believe that an
occupation, directly preparing for art, very
rarely can be continued in life. They call it,
therefore, aimless pastime without favorable
consequences, either for internal development
or external happiness.
If it must be admitted that the soiling of
the hands and clothing cannot always be
avoided, we hold that for this very reason,
this occupation is a capital one, for it will
give an opportunity to accustom the children
to care, order and cleanliness, provided the
teacher herself takes care to develop the sense
of the pupils, for these virtues, in connection
with this occupation ; as on all other occasions,
she should strive to excite the sense of clean-
liness as well as purity. Certainly, parts of
the adhesive clay will stick to the little fingers
and nails of the children, and their wooden
knives ; but, pray, what harm can grow out of
this? The child may learn even from this
fact. It may be remarked in connection with
it, that the callous hand of the husbandman,
the dirty blouse of the mechanic, only show
the occupation, and cannot take aught from
the inner worth of a man. As regards the ob-
jection to this occupation as aimless and
without result, it should be considered that
occupation with the beautiful, even in its
crudest beginnings, always bears good fruit,
because it prepares the individual for a true
appreciation and noble enjoyment of the
same. Just in this the significance of Froebel's
educational idea partly rests, that it strives to
open every human heart for the beautiful
and good — that it particularly is intended to
elevate the social position of the laboring
classes, by means of education, not only in
regard to knowledge and skill, but also, in
regard to a development of refinement and
feeling.
Representing, imitating, creating, or trans-
forming in general, is the child's greatest en-
joyment. Bread-crumbs are modeled by it
into balls, or objects of more complicated
form, and even when biting bits from its
cooky, it is the child's desire to produce
for?n. If a piece of wax, putty, or other plia-
ble matter, falls into its hands, it is kneaded
until it assumes a form, of which they may
assert that it represents a baby, — the dog
Roamer, or what not ! Wet sand, they press
into their little cooking utensils, when playing
"house-keeping," and pass off the forms as
puddings, tarts, etc. ; in one word, most chil-
dren are born sculptors. Could this fact have
escaped Froebel's keen observation? He
has here provided the means to satisfy this
desire of the child, to develop also this talent,
in its very awakening.
According to Froebel's principle, the first
exercises in modeling are the representation
of the fourteen stereometric fundamental forms
74
GUIDE TO KINDER- GARTNERS.
of crystallization, which he presents in a box,
by themselves as models. Starting from the
cube the cylinder follows — then the sphere
pyramid with 3, 4 and 6 sides, the. prism in its
various formations of planes, the octahcdro?t
or decahedron and cosahedron, or bodies with
8, 12 and 20 equal sides or faces, etc., etc.
However interesting and instructive this course
may be, we prefer to begin with somewhat
simpler performances, leaving this branch of
this department for future time.
The child receives a small quantity of clay,
(wa.x may also be used,) a wooden knife, a
small board, and a piece of oiled paper, on
which it performs the work. If clay is used,
this material should be kept in wet rags, in
a cool place, and the object formed of it,
dried in the sun, or in a mildly-heated stove,
and then coated with gum arabic, or var-
nish, which gives them the appearance of
crockery.
First, the child forms a sphere, from which it
may produce many objects. If it attaches a
stem to it, it is a cherry ; if it adds depressions
and elevations, which represent the dried calyx,
it will look like an apple ; from it the pear, nut,
potato, a head, may be molded, etc. Many
small balls made to adhere to one another
may produce a bunch of grapes, (Figs.
i-S.)
From the ball or sphere, a cylindrical body
may be formed, by rolling on the board, usu-
ally called by the children a loaf of bread,
cigar, a candle, loaf of sugar, etc.
A bottle, a bag filled with flour or some-
thing else, can also easily be produced.
Very soon the child will present the cube,
an old acquaintance and playmate. From it,
it produces a house, a bo.x, a coffee-mill and
similar things. Soon other forms of life will
grow into existence, as plates, dishes, animals
and human beings, houses, churches, birds'
nests, etc., etc. If this occupation is intended
to be more than mere entertainment, it is
necessary to guide the activity of the child in
a definite direction.
The best direction to be followed in Froe-
bel's occupations is that for the development
of regular forms of bodies. Fundamental
form, of course, is the sphere. The child
represents it easily, if perhaps not exactly
true.
By pressing and assisted by his knife, the
one plane of the sphere is changed to several
planes, corners, edges, which produces the
cube. If the child changes its corners to
planes (indicated in Fig. 12,) a form of four-
teen sides is produced. If this process is
continued so that the planes of the cube are
changed to corners, the octahedron is the re-
sult, (Fig. 13.) By continued change of edges
to planes and of planes to corners, the most
important regular forms of crystallization will
be produced, which occupation, however, as
mentioned before, belongs rather to a higher
grade of school, and is therefore better
postponed until after the Kinder-Garten
training.
Some regular bodies are more easily
formed from the cylinder, the mediation be-
tween the sphere and cube. By a pressure of
the hand, or by means of his knife, the child
changes the one round plane to three or four
planes, and as many edges, producing thereby
the prism and the four-sided column.
If we change one of the planes of the cyl-
inder to a corner, by forming a round plane
from its center to the periphery of the plane,
we produce a cone. If we change the sur-
face of the cone to three or four planes, we
shall have a three or four sided pyramid. If
we act in the same manner with the other end
of the cylinder, we shall form a double cone,
and from it we may produce a three or four-
sided double pyramid, etc. If we act in an
opposite manner, destroy the edges of the
cylinder, we shall again have the sphere.
Well formed specimens may, to acquire
greater durability, be treated as indicated
previously. The production of forms and fig-
ures from soft and pliable material belongs,
undoubtedly, to the earliest and most natural
occupations of the human race, and has served
all plastic arts as a starting-point. The occu-
GUIDE TO KINDER-GARTNERS.
75
pation of modeling, then, is eminently fit to
carry into practice Froebel's idea that chil-
dren, in their occupations, have to pass through
all the general grades of development of hu-
man culture in a diminished scale. The
natural talent of the future architect or sculp-
tor, lying dormant in the child, must needs be
called forth and developed by this occupation,
as by a self-acting and inventing construction
and formation, all innate talents of the child
are made to grow into visible reality.
If we now cast a retrospective look upon
the means of occupation in the Kinder-
Garten, we find that the material progresses
form the solid and whole, in gradual steps to
its parts, until it arrives at the image upon
the plane, and its conditions as to line and
point. For the heavy material, fit only to be
placed upon the table in unchanged form,
(the building blocks,) a more flexible one
is substituted in the following occupations :
7vood is replaced hy paper. The paper plane
of the folding occupation, is replaced by the
paper strip of the weaving occupation, as line.
The wooden staff, or very thin ivire, is then
introduced for the purpose of executing per-
manent figures in connection with peas, repre-
senting the point. In place of this material
the dratcn line then appears, to which colors
are added. Perforating and embroidering
introduces another addition to the material
to create the images of fantasy, which, in the
paper cutting and mounting, again receive
new elements.
The modeling \n clay, or wax, affords the im-
mediate plastic artistic occupation, with the
most pliable material for the hand of the
child. Song introduces into the realm of
sound, when movement plays, gymnastics, and
dancing, help to educate the body, and insure
a harmonious development of all its parts.
In practicing the technical manual perform-
ances of the mechanic, such as boring,
piercing, cutting, measuring, uniting, forming,
drawings painting, and modeling, a foundation
of all future occupation of artisan and artist
— synonymous in past centuries — is laid. For
ornamentation especially, all elements are
found in the occupations of the Kinder-Gar-
ten. The forms of beauty in the paper-fold-
ing,/. /., serve as series of rosettes and or-
naments in relief, as architecture might em-
ploy them, without change. The productions
in the braiding department contain all con-
ditions of artistic weaving, nor does the cut-
ting of figures fail to afford richest material
for ornamentation of various kinds.
For every talent in man, means of develop-
ment are provided in the Kinder-Garten ma-
terial, opportunity for practice is constantly
given, and each direction of the mind finds
its starting-point in concrete things. No more
complete satisfaction, therefore, can be given
to the claim of modern pedagogism, that all
ideas should be founded on previous percep-
tion, derived from real objects, than is done in
the genuine Kinder-Garten.
Whosoever has acquired even a superfi-
cial idea only of the significance of Froebel's
means of occupation in the Kinder-Garten,
will be ready to admit that the ordinary play-
things of children can not, by any means, as
regards their usefulness, be compared with
the occupation material in the Kinder-Gar-
ten. That the former may, in a certain de-
gree, be made helpful in the development of
children, is not denied ; occasional good re-
sults with them, however, mostly always will
be found to be owing to the child's own in-
stinct rather than to the nature of the toy.
Planless playing, without guidance and super-
vision cannot prepare a child for the earnest
sides of life as well as for the enjoyment of
its harmless amusements and pleasures.
Like the plant, which, in the wilderness even,
draws from the soil its nutrition, so the child's
mind draws from its surroundings and the
means, placed at its command, its educational
food. But the rose-bush, nursed and cared
for in the garden by the skillful horticulturist
produces flowers, far more perfect and beau-
tiful than the wild growing sweet-briar. With-
out care neither mind nor body of the child
76
GUIDE TO KINDER-GARTNERS.
can be expected to prosper. As the latter
can not, for a healthful development, use all
kinds of food without careful selection, so
the mind for its higher cultivation requires a
still more careful choice of the means for its
development. The child's free choice is lim-
ited only in so far as it is necessary to limit
the amount of occupation material in order
to fit it for systematic application. The child
will find instinctively all that is requisite for
its mental growth, if the proper material only
be presented, and a guiding mind indicate its
most appropriate use in accordance with a
certain law.
Froebel's genius has admirably succeeded
in inventing the proper material as well as in
pointing out its most successful application to
prepare the child for all situations in future
life, for all branches of occupation in the
useful pursuits of mankind.
When the Kinder-Garten was first estab-
lished by him, it was prohibited in its original
form and its inventor driven from place to
place in his fatherland on account of his lib-
eral educational principles, to be carried out
in the Kinder Garten. The keen eye of mo-
narchial government officials quickly saw that
such institution could not turn out willing
subjects to tyrannical oppression, and the ru-
lers "-^by the grace of God,'' tolerated the
Kinder-Garten, only when public opinion de-
clared too strongly in its favor.
In pleading the cause of the Kinder-Gar-
ten on the soil of republican America, is it
asking too much that all may help in extend-
ing to the future generation the benefits which
may be derived from an institution so emi-
nently fit to educate free citizens of a free
country ?
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P A- R T T .
PARADISE OF C!HlLDHOOD
A MAMAI. Kdli SKl.|--IXSTl!L-ClIo.\ l.V I'KIKDUICII KUOKIil- L';
KDrCATloNAl, I'UIXCll'I.KS.
(jiiide to Kinder-Gartners.
E I) W A R D W I E B E .
WITH SEVENTY- FOUR PLATES OF ILLUSTRATIONS.
.MILTON ]}KAULEY >!c COMPANY.
SIMilN(il-lKLl). .MASS.
PART IV.
PARA DISE OF CHILDHOOD :
A MANUAL Fol! SKLF-TN'STRUCTIOX IX FRIEnRICII FliOEBEL'S
EDUCATIONAL PRINCIPLES,
AND A PRACTfCAr
(jiiide toKinder-Grartners.
E D W A Pv D \V I E B PJ
WITH SEVENTY- FOUR PLATES OF ILLUSTRATIONS.
MILTON BllADLKY & COMPANY
SPUINCI'IKLl). MASS.
GIFTS. OR OCCUPATION MATERIAL FOR THE
IK I H D E m«ll A»1PS».
O0R high' estimation nl' llic tiiorits of tills system of education, lias iiuliicoil us to fit up tlic macliincr.v and
fixtures necessary for the |ir.idiutl(in of the Occiipatiox Matkkiai. in an economical and superior manner.
As the several (iifts have lneii prepared under the direction and liy tlie sii^'sestions of the most conipolent
teachers of Kinder-lJartcn in tliis country, we believe they will meet with universal favor; hut any sugiiestions
from Practical Kinder-Gartners, will be" thankfully received, and, if considered advantageous, will immediately
be embodied in our manufactures. Price Lists furnislied to Dealers and Teachers on application.
THE GREAT EDUCATIONAL CxAME OF
Wi: have purchased from the Inventor the entire Patent on the above Wii\-i)i;Rrt:i, ('o.miu
STROCTios AM) AJirsF.MF.NT, bv wliicli the jiriiiciples of
ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION
Are embodied in one of the most fascinating Games ever devised for Youth or Adults. There
this will ]irove the most popular I'arlor Amu.sement even invented. Price §0.(K).
THE NEW SCRIPTURE GAME OF
A Combination- op
CfniflOlli* Bible Qli®^1li#«|i
In a very pleasine; and Instructive Game.
-^JVIaqic ^quare^ and -^o^aic ^ablet^,
Fon Recreation, Kntertainineiit and Instruction, presenting some curious puzzles in the iirojierties of numbers;
adapted for use in families and school>,
HY
EDWARn W. OII.MAM.
Prof. Lyman of Yale College says in a note to the author of this work :
"Your device of 'Magic T.tblets' strikes me as one well fitted to aflbrd instruction ,and entertainment for tlie
young, and to become popular as an evening amusement. If it shall give to the lovers of mathematical puzzles
half Tlie gratification which I received when a boy from Magic S(|uares as commonly exhibited, the young people
will have abundant reason tft thank you for your imjiroved method of presentation.
" The talili'ts and book of problems are put u)) in a neat box complete." Price each, .SLOO.
THE ZOETROPE,
TImt OPTICAL WOXOKR— always new, with New Pictures.
ritOF. BOVEJR'S
LATEST MANUAL OF CROQUET,
FOR THE FIELD OR THE PARLOR, ILLUSTRATED.
Send 10 CEN-TS for the CnOQiin .Maxuat, and complete I'rice List of Games, etc. : or a Stamji for the Price Lists.
MILTON BRADLKV k (().,
Spi'iDff/ield. Mass.
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